which expression is equivalent to $left(\frac{x^{-4}y}{x^{-9}y^{5}}\right)^{-2}$? assume $x\neq0,y\neq0$.\n$\…

which expression is equivalent to $left(\frac{x^{-4}y}{x^{-9}y^{5}}\right)^{-2}$? assume $x\neq0,y\neq0$.\n$\frac{y^{8}}{x^{10}}$\n$\frac{x^{5}}{y^{7}}$\n$\frac{x^{5}}{y^{4}}$\n$\frac{x}{y^{7}}$

which expression is equivalent to $left(\frac{x^{-4}y}{x^{-9}y^{5}}\right)^{-2}$? assume $x\neq0,y\neq0$.\n$\frac{y^{8}}{x^{10}}$\n$\frac{x^{5}}{y^{7}}$\n$\frac{x^{5}}{y^{4}}$\n$\frac{x}{y^{7}}$

Answer

Explanation:

Step1: Simplify the fraction inside the parentheses

Use the quotient - rule of exponents $\frac{a^m}{a^n}=a^{m - n}$. So, $\frac{x^{-4}y}{x^{-9}y^{5}}=x^{-4-(-9)}y^{1 - 5}=x^{5}y^{-4}$.

Step2: Apply the power - of - a - power rule

Use the rule $(a^m)^n=a^{mn}$. So, $(x^{5}y^{-4})^{-2}=x^{5\times(-2)}y^{-4\times(-2)}$.

Step3: Calculate the exponents

$x^{5\times(-2)}y^{-4\times(-2)}=x^{-10}y^{8}=\frac{y^{8}}{x^{10}}$.

Answer:

$\frac{y^{8}}{x^{10}}$