Processing Math: 86%
1.3 Exercises
From Förberedande kurs i matematik 1
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{| border="0" cellspacing="0" cellpadding="0" height="30" width="100%" | {| border="0" cellspacing="0" cellpadding="0" height="30" width="100%" | ||
| style="border-bottom:1px solid #000" width="5px" | | | style="border-bottom:1px solid #000" width="5px" | | ||
- | {{ | + | {{Not selected tab|[[1.3 Powers|Theory]]}} |
- | {{ | + | {{Selected tab|[[1.3 Exercises|Exercises]]}} |
| style="border-bottom:1px solid #000" width="100%"| | | style="border-bottom:1px solid #000" width="100%"| | ||
|} | |} | ||
- | === | + | ===Exercise 1.3:1=== |
<div class="ovning"> | <div class="ovning"> | ||
- | + | Calculate | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
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|width="25%"| <math>\Bigl(\displaystyle \frac{2}{3}\Bigr)^{-3}</math> | |width="25%"| <math>\Bigl(\displaystyle \frac{2}{3}\Bigr)^{-3}</math> | ||
|} | |} | ||
- | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Answer 1.3:1|Solution a|Solution 1.3:1a|Solution b|Solution 1.3:1b|Solution c|Solution 1.3:1c|Solution d|Solution 1.3:1d}} |
- | === | + | ===Exercise 1.3:2=== |
<div class="ovning"> | <div class="ovning"> | ||
- | + | Write each of the following as a power of <math>2</math> | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
|width="33%"| <math>2\cdot4\cdot8</math> | |width="33%"| <math>2\cdot4\cdot8</math> | ||
|b) | |b) | ||
- | |width="33%"| <math>0{ | + | |width="33%"| <math>0\textrm{.}25</math> |
|c) | |c) | ||
|width="33%"| <math>1</math> | |width="33%"| <math>1</math> | ||
|} | |} | ||
- | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Answer 1.3:2|Solution a|Solution 1.3:2a|Solution b|Solution 1.3:2b|Solution c|Solution 1.3:2c}} |
- | === | + | ===Exercise 1.3:3=== |
<div class="ovning"> | <div class="ovning"> | ||
- | + | Write each of the following as a power of <math>3</math> | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
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|width="20%"| <math>\displaystyle \frac{3}{9^2}</math> | |width="20%"| <math>\displaystyle \frac{3}{9^2}</math> | ||
|} | |} | ||
- | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Answer 1.3:3|Solution a|Solution 1.3:3a|Solution b|Solution 1.3:3b|Solution c|Solution 1.3:3c|Solution d|Solution 1.3:3d|Solution e|Solution 1.3:3e}} |
- | === | + | ===Exercise 1.3:4=== |
<div class="ovning"> | <div class="ovning"> | ||
- | + | Calculate | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
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||<math>625\cdot(5^{8}+5^{9})^{-1}</math> | ||<math>625\cdot(5^{8}+5^{9})^{-1}</math> | ||
|} | |} | ||
- | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Answer 1.3:4|Solution a|Solution 1.3:4a|Solution b|Solution 1.3:4b|Solution c|Solution 1.3:4c|Solution d|Solution 1.3:4d|Solution e|Solution 1.3:4e}} |
- | === | + | ===Exercise 1.3:5=== |
<div class="ovning"> | <div class="ovning"> | ||
- | + | Calculate | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
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|| <math>\left(47^{2/3} \right) ^{3}</math> | || <math>\left(47^{2/3} \right) ^{3}</math> | ||
|e) | |e) | ||
- | ||<math>3^{1{ | + | ||<math>3^{1\textrm{.}4}\cdot3^{0\textrm{.}6}</math> |
|f) | |f) | ||
||<math>\bigl( 125 ^{1/3} \bigr)^2\cdot \bigl( 27^{1/3} \bigr)^{-2}\cdot9^{1/2}</math> | ||<math>\bigl( 125 ^{1/3} \bigr)^2\cdot \bigl( 27^{1/3} \bigr)^{-2}\cdot9^{1/2}</math> | ||
|} | |} | ||
- | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Answer 1.3:5|Solution a|Solution 1.3:5a|Solution b|Solution 1.3:5b|Solution c|Solution 1.3:5c|Solution d|Solution 1.3:5d|Solution e|Solution 1.3:5e|Solution f|Solution 1.3:5f}} |
- | === | + | ===Exercise 1.3:6=== |
<div class="ovning"> | <div class="ovning"> | ||
- | + | In each of the following cases, determine which is the larger of the two numbers. | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
- | |width="33%" | <math>256^{1/3}\ </math> | + | |width="33%" | <math>256^{1/3}\ </math> and <math>\ 200^{1/3} </math> |
|b) | |b) | ||
- | |width="33%" | <math>0{ | + | |width="33%" | <math>0\textrm{.}5^{-3}\ </math> and <math>\ 0\textrm{.}4^{-3} </math> |
|c) | |c) | ||
- | |width="33%" | <math>0{ | + | |width="33%" | <math>0\textrm{.}2^5\ </math> and <math>\ 0\textrm{.}2^{7} </math> |
|- | |- | ||
|d) | |d) | ||
- | || <math>400^{1/3}\ </math> | + | || <math>400^{1/3}\ </math> and <math>\ \bigl(5^{1/3}\bigr)^{4} </math> |
|e) | |e) | ||
- | ||<math>125^{1/2}\ </math> | + | ||<math>125^{1/2}\ </math> and <math>\ 625^{1/3} </math> |
|f) | |f) | ||
- | ||<math>2^{56}\ </math> | + | ||<math>2^{56}\ </math> and <math>\ 3^{40} </math> |
|} | |} | ||
- | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Answer 1.3:6|Solution a|Solution 1.3:6a|Solution b|Solution 1.3:6b|Solution c|Solution 1.3:6c|Solution d|Solution 1.3:6d|Solution e|Solution 1.3:6e|Solution f|Solution 1.3:6f}} |
Current revision
Theory | Exercises |
Exercise 1.3:1
Calculate
a) | ![]() | b) | ![]() | c) | | d) | ![]() ![]() |
Answer | Solution a | Solution b | Solution c | Solution d
Exercise 1.3:2
Write each of the following as a power of
a) | ![]() ![]() | b) | | c) | |
Answer | Solution a | Solution b | Solution c
Exercise 1.3:3
Write each of the following as a power of
a) | | b) | | c) | | d) | | e) | |
Answer | Solution a | Solution b | Solution c | Solution d | Solution e
Exercise 1.3:4
Calculate
a) | ![]() | b) | ![]() ![]() | c) | ![]() |
d) | ![]() | e) | ![]() |
Answer | Solution a | Solution b | Solution c | Solution d | Solution e
Exercise 1.3:5
Calculate
a) | ![]() | b) | ![]() | c) | ![]() |
d) | ![]() ![]() ![]() | e) | ![]() | f) | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f
Exercise 1.3:6
In each of the following cases, determine which is the larger of the two numbers.
a) | ![]() ![]() | b) | | c) | |
d) | ![]() | e) | \displaystyle 125^{1/2}\ and \displaystyle \ 625^{1/3} | f) | \displaystyle 2^{56}\ and \displaystyle \ 3^{40} |
Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f