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Övn 1 - Versionshistorik
2026-05-16T18:16:42Z
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KTH.SE:u1xsetv1 den 25 juni 2007 kl. 08.42
2007-06-25T08:42:49Z
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<td colspan='2' width='50%' align='center' style="background-color: white;">← Äldre version</td>
<td colspan='2' width='50%' align='center' style="background-color: white;">Versionen från 25 juni 2007 kl. 08.42</td>
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<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><span style="color: red; font-weight: bold;">_NOTOC_</span></td><td>+</td><td style="background: #cfc; font-size: smaller;"><span style="color: red; font-weight: bold;">__NOTOC__</span></td></tr>
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<tr><td> </td><td style="background: #eee; font-size: smaller;">==Övning 1.1:1==</td><td> </td><td style="background: #eee; font-size: smaller;">==Övning 1.1:1==</td></tr>
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KTH.SE:u1xsetv1
http://wiki.math.se/wikis/sf0600_0701/index.php?title=%C3%96vn_1&diff=2197&oldid=prev
KTH.SE:u1xsetv1: Ny sida: _NOTOC_ ==Övning 1.1:1== <div class="ovning"> Beräkna (utan hjälp av räknedosa) <table width="100%" cellspacing="10px"> <tr align="left"> <td class="ntext">a)</td> <td class="ntext" wi...
2007-06-25T08:41:21Z
<p>Ny sida: _NOTOC_ ==Övning 1.1:1== <div class="ovning"> Beräkna (utan hjälp av räknedosa) <table width="100%" cellspacing="10px"> <tr align="left"> <td class="ntext">a)</td> <td class="ntext" wi...</p>
<p><b>Ny sida</b></p><div>_NOTOC_<br />
<br />
==Övning 1.1:1==<br />
<div class="ovning"><br />
Beräkna (utan hjälp av räknedosa)<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$3-7-4+6-5$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$3-(7-4)+(6-5)$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$3-(7-(4+6)-5)$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">$3-(7-(4+6))-5$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
<div class="svar"><br />
<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$-7$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$1$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$11$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">$1$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
<br />
</div><br />
<br />
==Övning 1.1:2==<br />
<div class="ovning"><br />
Beräkna (utan hjälp av räknedosa)<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$(3-(7-4))(6-5)$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$3-(((7-4)+6)-5)$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$3\cdot(-7)-4\cdot(6-5)$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">$3\cdot(-7)-(4+6)/(-5)$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
<div class="svar"><br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$0$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$-1$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$-25$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">$-19$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 1.1:3==<br />
<div class="ovning"><br />
Vilka av följande tal tillhör de naturliga talen? heltalen?<br />
rationella talen? irrationella talen? Förenkla först!<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$8$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$-4$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$8-4$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="33%">$4-8$</td><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="33%">$8(-4)$</td><br />
<td class="ntext">f)</td><br />
<td class="ntext" width="33%">$(-8)(-4)$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">g)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{4}{-8}$</td><br />
<td class="ntext">h)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{-8}{-4}$</td><br />
<td class="ntext">i)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{\sqrt{2}}{3}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">j)</td><br />
<td class="ntext" width="33%">$\displaystyle \Bigl(\frac{4}{\sqrt{2}}\Bigr)^2$</td><br />
<td class="ntext">k)</td><br />
<td class="ntext" width="33%">$-\pi$</td><br />
<td class="ntext">l)</td><br />
<td class="ntext" width="33%">$\pi+1$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
<div class="svar"><br />
<table width="100%" cellspacing="10px"><br />
<tr><td height="5px"/></tr><br />
<tr align="left" valign="top"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">heltalen, rationella talen</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td><br />
</tr><br />
<tr align="left" valign="top"><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="33%">heltalen, rationella talen</td><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="33%">heltalen, rationella talen</td><br />
<td class="ntext">f)</td><br />
<td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td><br />
</tr><br />
<tr align="left" valign="top"><br />
<td class="ntext">g)</td><br />
<td class="ntext" width="33%">rationella talen</td><br />
<td class="ntext">h)</td><br />
<td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td><br />
<td class="ntext">i)</td><br />
<td class="ntext" width="33%">irrationella talen</td><br />
</tr><br />
<tr align="left" valign="top"><br />
<td class="ntext">j)</td><br />
<td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td><br />
<td class="ntext">k)</td><br />
<td class="ntext" width="33%">irrationella talen</td><br />
<td class="ntext">l)</td><br />
<td class="ntext" width="33%">irrationella talen</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 1.1:4==<br />
<div class="ovning"><br />
Ordna följande tal i storleksordning<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="100%">$\displaystyle 2,\ \frac{3}{5},\ \frac{5}{3}\ $ och $\ \displaystyle \frac{7}{3}$</td><br />
</tr><br />
<tr><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="100%">$\displaystyle -\frac{1}{2},\ -\frac{1}{5},\ -\frac{3}{10}\ $ och $\ \displaystyle -\frac{1}{3}$</td><br />
</tr><br />
<tr><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="100%">$\displaystyle \frac{1}{2},\ \frac{2}{3},\ \frac{3}{5},\ \frac{5}{8}\ $ och $\ \displaystyle \frac{21}{34}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
<div class="svar"><br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="100%">$\displaystyle \frac{3}{5}<\frac{5}{3}<2<\frac{7}{3}$</td><br />
</tr><br />
<tr><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="100%">$\displaystyle -\frac{1}{2}<-\frac{1}{3}<-\frac{3}{10}<-\frac{1}{5}$</td><br />
</tr><br />
<tr><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="100%">$\displaystyle \frac{1}{2}<\frac{3}{5}<\frac{21}{34}<\frac{5}{8}<\frac{2}{3}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 1.1:5==<br />
<div class="ovning"><br />
Ange decimalutvecklingen med tre korrekta decimaler till<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="25%">$\displaystyle \frac{7}{6}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="25%">$\displaystyle \frac{9}{4}$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="25%">$\displaystyle \frac{2}{7}$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="25%">$\sqrt{2}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
<div class="svar"><br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="25%">$1{,}167$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="25%">$2{,}250$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="25%">$0{,}286$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="25%">$1{,}414$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 1.1:6==<br />
<div class="ovning"><br />
Vilka av följande tal är rationella? Ange dem som en kvot mellan heltal.<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="100%">$3,14$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="100%">$3{,}1416\,1416\,1416\,\dots$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="100%">$0{,}2\,001\,001\,001\,\dots\,$ (därefter är var tredje decimal en 1:a och övriga 0)</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="100%">$0{,}10\,100\,1000\,10000\,1\dots\, $ (en 1:a, en 0:a, en 1:a, två 0:or, en 1:a, tre 0:or osv.)</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
<div class="svar"><br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="100%">Talet är rationellt och lika med $\,314/100 = 157/50\,$.</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="100%">Talet är rationellt och är lika med $\,31413/9999 = 10471/3333\,$.</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="100%">Talet är rationellt och lika med $\,1999/9990\,$.</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="100%">Talet är irrationellt.</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
<br />
==Övning 1.2:1==<br />
<div class="ovning"><br />
Skriv p&aring; gemensamt br&aring;kstreck <br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{7}{4}+\frac{11}{7}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{2}{7}-\frac{1}{5}$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{1}{6}-\frac{2}{5}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{1}{3}+\frac{1}{4}+\frac{1}{5}$</td><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{8}{7}+\frac{3}{4}-\frac{4}{3}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
<div class="svar"><br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{93}{28}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{3}{35}$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$\displaystyle -\frac{7}{30}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{47}{60}$</td><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{47}{84}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 1.2:2==<br />
<div class="ovning"><br />
Bestäm minsta gemensamma nämnare<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$\displaystyle \frac{1}{6}+\frac{1}{10}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$\displaystyle \frac{1}{4}-\frac{1}{8}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$\displaystyle \frac{1}{12}-\frac{1}{14}$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">$\displaystyle \frac{2}{45}+\frac{1}{75}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
<div class="svar"><br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$\displaystyle {30}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$\displaystyle {8}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$\displaystyle {84}$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">$\displaystyle {225}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 1.2:3==<br />
<div class="ovning"><br />
Beräkna följande uttryck genom att använda minsta gemensamma nämnare:<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$\displaystyle \frac{3}{20}+\frac{7}{50}-\frac{1}{10}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$\displaystyle \frac{1}{24}+\frac{1}{40}-\frac{1}{16}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
<div class="svar"><br />
<table width="100%" cellspacing="10px"><br />
<tr><td height="5px"/></tr><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$\displaystyle \frac{19}{100}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$\displaystyle \frac{1}{240}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 1.2:4==<br />
<div class="ovning"><br />
F&ouml;renkla f&ouml;ljande uttryck genom att skriva p&aring; gemensamt br&aring;kstreck. Br&aring;ket ska vara f&auml;rdigf&ouml;rkortat.<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$\displaystyle\frac{\displaystyle\frac{3}{5}}{\displaystyle\frac{7}{10}}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$\displaystyle\frac{\displaystyle\frac{2}{7}}{\displaystyle\frac{3}{8}}$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$\displaystyle\frac{\displaystyle\frac{1}{4}-\frac{1}{5}}{\displaystyle\frac{3}{10}}$</td><br />
</tr><tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
<div class="svar"><br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{6}{7}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{16}{21}$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{1}{6}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 1.2:5==<br />
<div class="ovning"><br />
F&ouml;renkla f&ouml;ljande uttryck genom att skriva p&aring; gemensamt br&aring;kstreck. Br&aring;ket ska vara f&auml;rdigf&ouml;rkortat.<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{2}{\displaystyle \frac{1}{7}\displaystyle -\frac{1}{15}}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$\displaystyle\frac{\displaystyle\frac{1}{2}\displaystyle+\frac{1}{3}}{\displaystyle\frac{1}{3}\displaystyle-\frac{1}{2}}$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$\displaystyle\frac{\displaystyle\frac{3}{10}\displaystyle-\frac{1}{5}}{\displaystyle\frac{7}{8}\displaystyle-\frac{3}{16}}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
<div class="svar"><br />
<table width="100%" cellspacing="10px"><br />
<tr><td height="5px"/></tr><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{105}{4}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$-5$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{8}{55}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 1.2:6==<br />
<br />
<div class="ovning"><br />
F&ouml;renkla $\ \,\displaystyle \frac{\displaystyle \frac{2}{\displaystyle 3+\frac{1}{2}}\displaystyle + \frac{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{4}\displaystyle -\frac{1}{3}}}{\displaystyle \frac{1}{2}\displaystyle - \frac{3}{\displaystyle 2-\frac{2}{7}}}$<br />
</div><br />
<br />
<div class="svar"><br />
<table align="center" width="100%"><tr><td class="ntext" align="center">$\displaystyle \frac{152}{35}$</td></tr></table> <br />
</div><br />
<br />
<br />
==&Ouml;vning 1.3:1==<br />
<br />
<div class="ovning"><br />
Ber&auml;kna <br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="25%">$2^3\cdot3^2$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="25%">$3^5\cdot9^{-2}$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="25%">$(-5)^3$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="25%">$\Bigl(\displaystyle \frac{2}{3}\Bigr)^{-3}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
<div class="svar"><br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="25%">$72$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="25%">$3$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="25%">$-125$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="25%">$\displaystyle \frac{27}{8}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 1.3:2==<br />
<br />
<div class="ovning"><br />
Skriv som en potens av 2<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$2\cdot4\cdot8$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$0{,}25$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$1$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
<div class="svar"><br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$2^6$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$2^{-2}$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$2^0$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 1.3:3==<br />
<br />
<div class="ovning"><br />
Skriv som en potens av 3<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="20%">$\displaystyle \frac{1}{3}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="20%">$243$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="20%">$9^2$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="20%">$\displaystyle \frac{1}{27}$</td><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="20%">$\displaystyle \frac{3}{9^2}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
<div class="svar"><br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="20%">$3^{-1}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="20%">$3^5$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="20%">$3^4$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="20%">$3^{-3}$</td><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="20%">$3^{-3}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 1.3:4==<br />
<br />
<div class="ovning"><br />
Ber&auml;kna<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$2^{9}\cdot2^{-7}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$3^{13}\cdot9^{-3}\cdot27^{\,-2}$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{5^{12}}{5^{-4}}\cdot(5^{2})^{-6}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="33%">$2^{2^{\scriptstyle3}}\cdot(-2)^{\scriptstyle-4}$</td><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="33%">$625\cdot(5^{8}+5^{9})^{-1}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
<div class="svar"><br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$4$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$3$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$625$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="33%">$16$</td><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{1}{3750}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 1.3:5==<br />
<br />
<div class="ovning"><br />
Ber&auml;kna<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$4^{1/2}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$4^{-1/2}$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$9^{3/2}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="33%">$\left(47^{2/3} \right) ^{3}$</td><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="33%">$3^{1{,}4}\cdot3^{0{,}6}$</td><br />
<td class="ntext">f)</td><br />
<td class="ntext" width="33%">$\bigl( 125 ^{1/3} \bigr)^2\cdot \bigl( 27^{1/3} \bigr)^{-2}\cdot9^{1/2}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
<div class="svar"><br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$2$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{1}{2}$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$27$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="33%">$2209$</td><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="33%">$9$</td><br />
<td class="ntext">f)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{25}{3}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
<br />
==&Ouml;vning 1.3:6==<br />
<div class="ovning"><br />
Avg&ouml;r vilket tal som &auml;r st&ouml;rst av <br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$256^{1/3}\ $ och $\ 200^{1/3}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$0{,}5^{-3}\ $ och $\ 0{,}4^{-3}$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$0{,}2^5\ $ och $\ 0{,}2^{7}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="33%">$400^{1/3}\ $ och $\ \bigl(5^{1/3}\bigr)^{4}$</td><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="33%">$125^{1/2}\ $ och $\ 625^{1/3}$</td><br />
<td class="ntext">f)</td><br />
<td class="ntext" width="33%">$2^{56}\ $ och $\ 3^{40}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
<div class="svar"><br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$256^{1/3}>200^{1/3}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$0{,}4^{-3}>0{,}5^{-3}$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$0{,}2^{5}>0{,}2^{7}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="33%">$\bigl(5^{1/3}\bigr)^{4}>400^{1/3}$</td><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="33%">$125^{1/2}>625^{1/3}$</td><br />
<td class="ntext">f)</td><br />
<td class="ntext" width="33%">$3^{40}>2^{56}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div></div>
KTH.SE:u1xsetv1