Question

if a power n=b then n root b is​

Answer 1

Answer:

nb.

Step-by-step explanation:

n=b is nb root so.........

Answer 2

SOLUTION

GIVEN

$\sf{ {a}^{n} = b \: }$

TO DETERMINE

$\sf{ \sqrt[n]{b} \: }$

FORMULA TO BE IMPLEMENTED

We are aware of the formula on indices that

$\sf{ { ({x}^{m}) }^{n} = {x}^{mn} \: }$

EVALUATION

Here it is given that

$\sf{ {a}^{n} = b \: }$

$\displaystyle \implies \sf{ {({a}^{n})}^{ \frac{1}{n} } = {b}^{ \frac{1}{n} } \: }$

$\displaystyle \implies \sf{ {a}^{(n \times \frac{1}{n} )} = {b}^{ \frac{1}{n} } \: } \: \bigg( \because {({x}^{m})}^{n} = {x}^{mn} \bigg)$

$\displaystyle \implies \sf{ {a}^{1} = {b}^{ \frac{1}{n} } \: }$

$\displaystyle \implies \sf{ {a} = {b}^{ \frac{1}{n} } \: }$

$\displaystyle \implies \sf{{b}^{ \frac{1}{n} } = a \: }$

$\displaystyle \implies \sf{ \sqrt[n]{b} = a \: }$

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