Question

Which of the following is the simplified form of fifth root of x times the fifth root of x times the fifth root of x times the fifth root of x?
x to the 1 over fifth power
x to the 4 over fifth power
x to the four over twentieth power
x

Answer 1

Answer:

$\large\boxed{x^\frac{4}{5}}$

Step-by-step explanation:

$\sqrt[n]{a}=a^\frac{1}{n}\Rightarrow\sqrt[5]{x}=x^\frac{1}{5}\\\\\sqrt[5]{x}\cdot\sqrt[5]{x}\cdot\sqrt[5]{x}\cdot\sqrt[5]{x}=x^\frac{1}{5}\cdot x^\frac{1}{5}\cdot x^\frac{1}{5}\cdot x^\frac{1}{5}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=x^{\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}}=x^\frac{4}{5}$

Answer 2

Answer:

$x^{\frac{4}{5}}$

Step-by-step explanation:

fifth root of x can be written in exponential for as:

$x^\frac{1}{5}$

$x^\frac{1}{5}$ times  $x^\frac{1}{5}$ times  $x^\frac{1}{5}$ times  $x^\frac{1}{5}$

WE apply exponential property to multiply it

a^m times a^n= a^{m+n}

$x^\frac{1}{5}$ times  $x^\frac{1}{5}$ times  $x^\frac{1}{5}$ times  $x^\frac{1}{5}$

$x^{\frac{1}{5} +\frac{1}{5}+\frac{1}{5}+\frac{1}{5}}$

The denominator of the fractions are same so we add the numerators

$x^{\frac{4}{5}}$