Question

What is the value of y^-5 and x^-3 for x = 2 and y = -4?

Answer 1

$a^{-n}=\dfrac{1}{a^n}\\\\x^{-3}=\dfrac{1}{x^3};\ y^{-5}=\dfrac{1}{y^5}\\\\\dfrac{y^{-5}}{x^{-3}}=\dfrac{1}{y^5}:\dfrac{1}{x^3}=\dfrac{1}{y^5}\cdot\dfrac{x^3}{1}=\dfrac{x^3}{y^5}\\\\x=2;\ y=-4=-2^2\\\\\dfrac{x^3}{y^5}=\dfrac{2^3}{(-2^2)^5}=\dfrac{2^3}{-2^{2\cdot5}}=\dfrac{2^3}{-2^{10}}=-\dfrac{1}{2^7}=\boxed{-\dfrac{1}{128}}\to\fbox{C.}$