Answer:
Option B is the correct option.
Step-by-step explanation:
Given the expression
[tex]\frac{\sqrt[3]{x^5}}{\sqrt[3]{x^7}}[/tex]
Apply radical rule:
[tex]\frac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\frac{a}{b}}[/tex]
so
[tex]\frac{\sqrt[3]{x^5}}{\sqrt[3]{x^7}}=\sqrt[3]{\frac{x^5}{x^7}}[/tex]
Apply radical rule:
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
so
[tex]=\sqrt[3]{\frac{1}{x^2}}[/tex] ∵ [tex]\frac{x^5}{x^7}=x^{5-7}[/tex]
[tex]=\frac{1}{x^{\frac{2}{3}}}[/tex]
Therefore, option B is the correct option.
