For questions like "What is the 12 th root of x would the answer be x2?

Step 1The definition is:xa=x1a.Hence, if&nbsp;a=1b, then:x1b=xb.As a consequence:x12=x2.Step 2Notice that&nbsp;a=1b&nbsp;implies that, if for example&nbsp;b=2291, then&nbsp;a=9122. If for example&nbsp;b=3, then&nbsp;a=13. And so on.

Step by step solution to "For questions like "What is the 12 th..."

High School
Algebra
Pre-Algebra
Decimals

Cazzaoro0w9

Answered question

2022-04-15

For questions like "What is the

\frac{1}{2}

th root of x would the answer be

x^{2}

Answer & Explanation

seskew192atp

Beginner2022-04-16Added 12 answers

Step 1
The definition is:
$\sqrt[a]{x} = x^{\frac{1}{a}} .$
Hence, if $a = \frac{1}{b}$ , then:
$\sqrt[\frac{1}{b}]{x} = x^{b} .$
As a consequence:
$\sqrt[\frac{1}{2}]{x} = x^{2} .$
Step 2
Notice that $a = \frac{1}{b}$ implies that, if for example $b = \frac{22}{91}$ , then $a = \frac{91}{22}$ . If for example $b = \sqrt{3}$ , then $a = \frac{1}{\sqrt{3}}$ . And so on.

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