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Q61.

Expert-verifiedFound in: Page 227

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.

The given property is:

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

The definition of exponent is: ${x}^{p}=\underset{}{\underset{p}{\underset{\u23df}{x\cdot x\cdot \mathrm{......}\cdot x}}}$

Using this property, we can write${a}^{m}=\underset{}{\underset{m}{\underset{\u23df}{a\cdot a\cdot \mathrm{......}\cdot a}}}$ and ${a}^{n}=\underset{}{\underset{n}{\underset{\u23df}{a\cdot a\cdot \mathrm{......}\cdot a}}}$.

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

$\underset{m}{\underset{\u23df}{a\cdot a\cdot \mathrm{......}\cdot a}}\cdot \underset{}{\underset{n}{\underset{\u23df}{a\cdot a\cdot \mathrm{......}\cdot a}}}=\underset{}{\underset{m+n}{\underset{\u23df}{a\cdot a\cdot \mathrm{......}\cdot a}}}$.

Then again using the definition of exponent we get:$\underset{}{\underset{m+n}{\underset{\u23df}{a\cdot a\cdot \mathrm{......}\cdot a}}}={a}^{m+n}$ .

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