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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q 143. (page 1055)

Explain why $\sqrt{x^{4}} = x^{2}$ Then explain why $\sqrt{x^{16}} = x^{8}$ .

Short Answer

Expert verified

We have proved that $\sqrt{x^{4}} = x^{2} and \sqrt{x^{16}} = x^{8}$ .

Step by step solution

Step 1. Given information.

The given statement is:

Explain why $\sqrt{x^{4}} = x^{2} and \sqrt{x^{16}} = x^{8}$ .

Step 2. Explain that x4=x2.

As we know that $(a^{m}) = a^{m 路 n}$ .

Therefore, we can say that:

${(x^{2})}^{2} = x^{4}$ ,

and $\sqrt{x^{4}} = x^{2}$

Step 3. Explain that x16=x8.

Since ${(x^{8})}^{2} = x^{16}$

then $\sqrt{x^{16}} = x^{8}$

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Explain why x4=x2 Then explain whyx16=x8.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Explain that x4=x2.

Step 3. Explain that x16=x8.

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Explain why $\sqrt{x^{4}} = x^{2}$ Then explain why $\sqrt{x^{16}} = x^{8}$ .