Question

8.Rewrite the expression using rational exponents.

Answer 1

Option B is the correct option.

Explanation:

Given the expression

`\frac{\sqrt[3]{x^5}}{\sqrt[3]{x^7}}`

Apply radical rule:

`\frac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{(a)/(b)}`

so

`\frac{\sqrt[3]{x^5}}{\sqrt[3]{x^7}}=\sqrt[3]{(x^5)/(x^7)}`

Apply radical rule:

`(x^a)/(x^b)=x^(a-b)`

so

`=\sqrt[3]{(1)/(x^2)}` ∵
`(x^5)/(x^7)=x^(5-7)`

`=\frac{1}{x^{(2)/(3)}}`

Therefore, option B is the correct option.