## Calculus with Applications (10th Edition)

Published by Pearson

# Chapter R - Algebra Reference - R.6 Exponents - R.6 Exercises: 19

#### Answer

$a^{3}b^{6}$

#### Work Step by Step

Step 1: When looking at this problem, you will see there are parenthesis around the whole fraction and that it is raised to the -3 power. These parenthesis mean that you distribute the -3 exponent to everything inside of the fraction. You do this by multiplying -3 by the other exponents connected to the values a and b separately. So, -1 * -3 = 3 2 * -3 = -6 Therefore, you end up with $\frac{a^{3}}{b^{-6}}$ Step 2: Once you distribute the -3, you notice that the a value becomes positive and the b value becomes negative. Since you cannot have a negative exponent in your final answer, you have to change the problem around to make the b value's exponent positive. You do this by moving the $b^{-6}$ from the denominator, to the numerator. It then becomes: $\frac{a^{3}\times{b^{6}}}{1}$ Step 3: The last step is to simplify the fraction. Since "a" and "b" are not like terms, you cannot combine them. Also, anything divided by 1 is just itself. Therefore, you can eliminate the fraction by getting rid of the 1 leaving $a^{3}\times{b^{6}}$ as your final answer.

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