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

`(\sqrt[5]{x})^4=x^(4)/(5)`

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^(m)/(n)`

`(\sqrt[5]{x})^4=x^(4)/(5)`