Question

Which of the following questions are equivalent to the answer below x 3/5

Answer 1

Answer:

$x^\frac{3}{5} = (x^3 )^\frac{1}{5}$

$x^\frac{3}{5} = \sqrt[5]{x^3}$

$x^\frac{3}{5} = (\sqrt[5]{x})^3$

Step-by-step explanation:

Given

$x^\frac{3}{5}$

Required

The equivalent expressions

We have:

$x^\frac{3}{5}$

Expand the exponent

$x^\frac{3}{5} = x^{ 3 * \frac{1}{5}}$

So, we have:

$x^\frac{3}{5} = (x^3 )^\frac{1}{5}$ ----- this is equivalent

Express 1/5 as roots (law of indices)

$x^\frac{3}{5} = \sqrt[5]{x^3}$ ------ this is equivalent

The above can be rewritten as:

$x^\frac{3}{5} = (\sqrt[5]{x})^3$ ------ this is equivalent