Question

8.Rewrite the expression using rational exponents.

Answer 1

Answer:

Option B is the correct option.

Step-by-step explanation:

Given the expression

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

Apply radical rule:

$\frac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\frac{a}{b}}$

so

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

Apply radical rule:

$\frac{x^a}{x^b}=x^{a-b}$

so

   $=\sqrt[3]{\frac{1}{x^2}}$         ∵  $\frac{x^5}{x^7}=x^{5-7}$

   $=\frac{1}{x^{\frac{2}{3}}}$

Therefore, option B is the correct option.