Question

Which of the following choices are equivalent to the expression below ? X^3/5

Answer 1

Answer:

A

C

D

Step-by-step explanation:

Given in the question an expression

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

We know that

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

here x = 3

        y = 5

so

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

When exponent power rule is applied we can say that

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

because

3/5 = 3*(1/5)

Thirdly,

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

Answer 2

ANSWER

The correct choices are A, C, D

EXPLANATION

The given expression is

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

Recall that,

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

This implies that,

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

Also,

$( {a}^{m} ) ^{n} = {a}^{mn}$

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

Or

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

The correct choices are A, C, D