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Q61.

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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

CRITICAL THINKING For Exercises 61 and 62, use the following proof of the Power of a Power Property.
What definition or property allows you to make each step of the proof?

The definition of exponent allows us to make each step of the proof.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step-1 – Given

The given property is:

Step-2 – To determine

We have to find: What definition or property allows you to make each step of the proof?

Step-3 – Calculation

The definition of exponent is: $x^{p} = \underset{}{\underset{p}{\underset{⏟}{x \cdot x \cdot ...... \cdot x}}}$

Using this property, we can write $a^{m} = \underset{}{\underset{m}{\underset{⏟}{a \cdot a \cdot ...... \cdot a}}}$ and $a^{n} = \underset{}{\underset{n}{\underset{⏟}{a \cdot a \cdot ...... \cdot a}}}$ .

Then using the associative property of multiplication, we can say:

$\underset{m}{\underset{⏟}{a \cdot a \cdot ...... \cdot a}} \cdot \underset{}{\underset{n}{\underset{⏟}{a \cdot a \cdot ...... \cdot a}}} = \underset{}{\underset{m + n}{\underset{⏟}{a \cdot a \cdot ...... \cdot a}}}$ .

Then again using the definition of exponent we get: $\underset{}{\underset{m + n}{\underset{⏟}{a \cdot a \cdot ...... \cdot a}}} = a^{m + n}$ .

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