Question

write in index form - square of Cuberoot of 5​

Answer 1

Given :   square of Cuberoot of 5​

To Find : write in index form

Solution:

square of Cuberoot of 5​

Cuberoot of 5​ = ∛5

square of Cuberoot of 5​ = (∛5)²

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

$\sqrt[n]{x}$  is root form

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

(∛5)²  =   $(5^{\frac{1}{3} })^2$

(xᵃ)ᵇ = (x)ᵃᵇ

Hence

$(5^{\frac{1}{3} })^2 =5^{\frac{2}{3}$

so index form of square of Cuberoot of 5​ is

$5^{\frac{2}{3}$

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