Mathematics: 8.Rewrite the expression using rational exponents.

8.Rewrite the expression using rational exponents. - id810363180, carethegymnast8954

IIIKiXIII

17.03.2022

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:

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

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

Apply radical rule:

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

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

$=\frac{1}{x^{\frac{2}{3}}}$

Therefore, option B is the correct option.

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