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

Which of the following is the simplified form of [1] fifth root of x times the [2] fifth root of x times [3] the fifth root of x times [4] the fifth root of x?

That's

$( \sqrt[5] x)^4 = x^{\frac 4 5}$

That looks like the second choice.

Answer 2

Answer:

$(\sqrt[5]{x})^4=x^\frac{4}{5}$

Step-by-step explanation:

$\sqrt[5]{x} *\sqrt[5]{x} *\sqrt[5]{x} *\sqrt[5]{x}$

Simplify the given expression

we have fifth root repeating 4 times , so we put exponent 4

like $x*x*x*x= x^4$

$\sqrt[5]{x} *\sqrt[5]{x} *\sqrt[5]{x} *\sqrt[5]{x}$

$(\sqrt[5]{x})^4$

Now we convert radical form into exponential form

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

$(\sqrt[5]{x})^4=x^\frac{4}{5}$