Question

What is equivalent to 3√125 ^x?

125 1/3 ^x

125 1/3x

125 3x

125(1/3)^x

Answer 1

Option D)
`((125)^{(1)/(3)})^x`

Explanation:

We are given the following in the question:

`(^3√(125))^x`

We have to write and equivalent expression for the same.

Exponential properties:

`^3√(a) = a^{(1)/(3)}\\(a^x)^y = a^(xy)`

Using the above properties, we can write:

`(^3√(125))^x\\=((125)^{(1)/(3)})^x\\=(125)^{(x)/(3)}`

Thus, the correct option is

Option D)
`((125)^{(1)/(3)})^x`