Question

Which expression is equivalent to (x^-4y/x^-9y^5)^-2

Answer 1

Answer:

$\large\boxed{x^{-10}y^8=\dfrac{y^8}{x^{10}}}$

Step-by-step explanation:

$\left(\dfrac{x^{-4}y}{x^{-9}y^5}\right)^{-2}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\\left(x^{-4-(-9)}y^{1-5}\right)^{-2}=(x^5y^{-4})^{-2}\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=(x^5)^{-2}(y^{-4})^{-2}=x^{(5)(-2)}y^{(-4)(-2)}=x^{-10}y^8\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{y^8}{x^{10}}$