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Expert-verified Found in: Page 227 ### Algebra 2

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

See the step by step solution

## 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:$\underset{}{\underset{m+n}{\underset{⏟}{a\cdot a\cdot ......\cdot a}}}={a}^{m+n}$ . ### Want to see more solutions like these? 