Question

Express in index form
Eight root of 100

Answer 1

Eight root of 100  in index form is $(100)^{\frac{1}{8} }$   or $(10)^{\frac{1}{4} }$

Given : Eight root of 100

To Find : Express in index form

Solution:

Eight root of 100

= $\sqrt[8]{100}$

$\sqrt[n]{x} =x^{\frac{1}{n} }$

$\sqrt[n]{x}$ is root form

$x^{\frac{1}{n} }$  is index form  where x  is the base  and 1/n is the index

$\sqrt[8]{100} = (100)^{\frac{1}{8} }$  

But it can be simplified further

as  100 = 10²

$\sqrt[8]{100} = (10^2)^{\frac{1}{8} }$  

Using Law of exponent   $(x^a)^b =x^{a.b}$

$\sqrt[8]{100} = (10)^{\frac{1}{4} }$

Hence ,   Eight root of 100  in index form is $(100)^{\frac{1}{8} }$   or $(10)^{\frac{1}{4} }$

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