Question

which exponential expression is equivalent to \\(\left(\sqrt5{y}\
ight)^4\\)?

choose 1 answer:

\\(\boldsymbol{\text{a}}\\) \\(y^{\frac{4}{5}}\\)

\\(\boldsymbol{\text{b}}\\) \\(y^{\frac{5}{4}}\\)

\\(\boldsymbol{\text{c}}\\) \\(\frac{y^4}{y^5}\\)

\\(\boldsymbol{\text{d}}\\) \\(\frac{y^5}{y^4}\\)

Explanation:

Step1: Convert root to exponent

$\sqrt[5]{y} = y^{\frac{1}{5}}$

Step2: Apply power rule

$(y^{\frac{1}{5}})^4 = y^{\frac{1}{5} \times 4} = y^{\frac{4}{5}}$

Answer:

A. $y^{\frac{4}{5}}$