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Q40.

Expert-verified

Algebra 2

Found in: Page 227

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

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 by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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,

$\begin{matrix} \frac{30 a^{- 2} b^{- 6}}{60 a^{- 6} b^{- 8}} = \frac{a^{- 2} b^{- 6}}{2 a^{- 6} b^{- 8}} \\ = \frac{{(a)}^{- 2 - (- 6)} {(b)}^{- 6 - (- 8)}}{2} .... (Using \frac{x^{a}}{x^{b}} = x^{a - b}) \\ = \frac{{(a)}^{4} {(b)}^{2}}{2} \\ = \frac{a^{4} b^{2}}{2} \end{matrix}$

Step 3. Conclusion.

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

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