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Q40.

Expert-verified
Found in: Page 227

### Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903

# Simplify $\frac{30{a}^{-2}{b}^{-6}}{60{a}^{-6}{b}^{-8}}$ assuming that no variable equal to 0 .

The simplified value of expression is $\frac{{a}^{4}{b}^{2}}{2}$ .

See the step by step solution

## Step 1. Write down the given expression.

The given expression to simplify is$\frac{30{a}^{-2}{b}^{-6}}{60{a}^{-6}{b}^{-8}}$ .

## Step 2. Simplify the given expression.

Simplifying$\frac{30{a}^{-2}{b}^{-6}}{60{a}^{-6}{b}^{-8}}$ gives,

$\begin{array}{c}\frac{30{a}^{-2}{b}^{-6}}{60{a}^{-6}{b}^{-8}}=\frac{{a}^{-2}{b}^{-6}}{2{a}^{-6}{b}^{-8}}\\ =\frac{{\left(a\right)}^{-2-\left(-6\right)}{\left(b\right)}^{-6-\left(-8\right)}}{2}....\left(\text{Using}\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\right)\\ =\frac{{\left(a\right)}^{4}{\left(b\right)}^{2}}{2}\\ =\frac{{a}^{4}{b}^{2}}{2}\end{array}$

## Step 3. Conclusion.

The simplified value of expression is $\frac{{a}^{4}{b}^{2}}{2}$ .