1.3 Exercises
From Förberedande kurs i matematik 1
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| - | {{ | + | {{Not selected tab|[[1.3 Powers|Theory]]}} |
| - | {{ | + | {{Selected tab|[[1.3 Exercises|Exercises]]}} |
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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:Answer|Answer 1.3:1|Solution a| | + | </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}} |
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|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:Answer|Answer 1.3:2|Solution a| | + | </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}} |
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|width="20%"| <math>\displaystyle \frac{3}{9^2}</math> | |width="20%"| <math>\displaystyle \frac{3}{9^2}</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Answer|Answer 1.3:3|Solution a| | + | </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}} |
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||<math>625\cdot(5^{8}+5^{9})^{-1}</math> | ||<math>625\cdot(5^{8}+5^{9})^{-1}</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Answer|Answer 1.3:4|Solution a| | + | </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}} |
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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:Answer|Answer 1.3:5|Solution a| | + | </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=== | ===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> and <math>\ 200^{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) | ||
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||<math>2^{56}\ </math> and <math>\ 3^{40} </math> | ||<math>2^{56}\ </math> and <math>\ 3^{40} </math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Answer|Answer 1.3:6|Solution a| | + | </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) | \displaystyle 2^3\cdot3^2 | b) | \displaystyle 3^5\cdot9^{-2} | c) | \displaystyle (-5)^3 | d) | \displaystyle \Bigl(\displaystyle \frac{2}{3}\Bigr)^{-3} |
Answer
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Solution a
Solution b
Solution c
Solution d
Exercise 1.3:2
Write each of the following as a power of \displaystyle 2
| a) | \displaystyle 2\cdot4\cdot8 | b) | \displaystyle 0\textrm{.}25 | c) | \displaystyle 1 |
Answer
Solution a
Solution b
Solution c
Exercise 1.3:3
Write each of the following as a power of \displaystyle 3
| a) | \displaystyle \displaystyle \frac{1}{3} | b) | \displaystyle 243 | c) | \displaystyle 9^2 | d) | \displaystyle \displaystyle \frac{1}{27} | e) | \displaystyle \displaystyle \frac{3}{9^2} |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Exercise 1.3:4
Calculate
| a) | \displaystyle 2^{9}\cdot2^{-7} | b) | \displaystyle 3^{13}\cdot9^{-3}\cdot27^{\,-2} | c) | \displaystyle \displaystyle \frac{5^{12}}{5^{-4}}\cdot(5^{2})^{-6} |
| d) | \displaystyle 2^{2^{\scriptstyle3}}\cdot(-2)^{\scriptstyle-4} | e) | \displaystyle 625\cdot(5^{8}+5^{9})^{-1} |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Exercise 1.3:5
Calculate
| a) | \displaystyle 4^{1/2} | b) | \displaystyle 4^{-1/2} | c) | \displaystyle 9^{3/2} |
| d) | \displaystyle \left(47^{2/3} \right) ^{3} | e) | \displaystyle 3^{1\textrm{.}4}\cdot3^{0\textrm{.}6} | f) | \displaystyle \bigl( 125 ^{1/3} \bigr)^2\cdot \bigl( 27^{1/3} \bigr)^{-2}\cdot9^{1/2} |
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) | \displaystyle 256^{1/3}\ and \displaystyle \ 200^{1/3} | b) | \displaystyle 0\textrm{.}5^{-3}\ and \displaystyle \ 0\textrm{.}4^{-3} | c) | \displaystyle 0\textrm{.}2^5\ and \displaystyle \ 0\textrm{.}2^{7} |
| d) | \displaystyle 400^{1/3}\ and \displaystyle \ \bigl(5^{1/3}\bigr)^{4} | 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
