which expression is equivalent to $\\left(\\frac{x^{-6}}{x^{2}}\\right)^{3}$?\n$\\frac{1}{x}$\n$\\frac{1}{x^{…

which expression is equivalent to $\\left(\\frac{x^{-6}}{x^{2}}\\right)^{3}$?\n$\\frac{1}{x}$\n$\\frac{1}{x^{5}}$\n$\\frac{1}{x^{9}}$\n$\\frac{1}{x^{24}}$

which expression is equivalent to $\\left(\\frac{x^{-6}}{x^{2}}\\right)^{3}$?\n$\\frac{1}{x}$\n$\\frac{1}{x^{5}}$\n$\\frac{1}{x^{9}}$\n$\\frac{1}{x^{24}}$

Answer

Explanation:

Step1: Simplify the fraction inside the parentheses

Use the rule $\frac{x^m}{x^n}=x^{m - n}$. So, $\frac{x^{-6}}{x^{2}}=x^{-6-2}=x^{-8}$.

Step2: Raise the result to the power of 3

Use the rule $(x^m)^n=x^{mn}$. So, $(x^{-8})^3=x^{-8\times3}=x^{-24}$.

Step3: Rewrite with positive exponent

Use the rule $x^{-n}=\frac{1}{x^{n}}$. So, $x^{-24}=\frac{1}{x^{24}}$.

Answer:

$\frac{1}{x^{24}}$