Question

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

Answer 1

ANSWER

The correct choices are A, C, D

EXPLANATION

The given expression is


`{x}^{ (3)/(5) }`

Recall that,


`{a}^{ (m)/(n) } = \sqrt[n]{ {a}^(m) }`

This implies that,


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

Also,


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


`{x}^{ (3)/(5) } =( {x}^( 3) ) ^{ (1)/(5) }`

Or


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

The correct choices are A, C, D

Answer 2

A

C

D

Explanation:

Given in the question an expression

`x^{(3)/(5)}`

We know that

`n^{(x)/(y)} = \sqrt[y]{n^(x)}`

here x = 3

y = 5

so

`n^{(3)/(5)}=\sqrt[5]{n^(3) }`

When exponent power rule is applied we can say that

`x^{(3)/(5)}=(x^(3))^{(1)/(5) }`

because

3/5 = 3*(1/5)

Thirdly,

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