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Q39.

Expert-verified

Algebra 2

Found in: Page 528

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

Simplify the expression ${(5^{\sqrt{2}})}^{\sqrt{8}}$ .

The simplified value of expression is 625.

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 is ${(5^{\sqrt{2}})}^{\sqrt{8}}$ .

Step 2. Simplify the expression.

The given expression ${(5^{\sqrt{2}})}^{\sqrt{8}}$ is simplified as:

$\begin{array}{l} {(5^{\sqrt{2}})}^{\sqrt{8}} = {(5)}^{\sqrt{2} \times \sqrt{8}} \\ = {(5)}^{\sqrt{16}} \\ = {(5)}^{4} \\ = 625 \end{array}$

Step 3. Conclusion.

The simplified value of expression is $625$ .

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