Question

Which expression is equivalent to -9x^-1y^-1 / -15x^5 y^-3 Assume x = 0 y = 0

Answer 1

For this case we have the following expression:
   -9x ^ -1y ^ -1 / -15x ^ 5 y ^ -3
 For power properties we have:
   -9x ^ (- 1-5) y ^ (- 1 - (- 3)) / - 15
 Rewriting we have:
   9x ^ (- 6) y ^ (- 1 + 3) / 15
   3x ^ (- 6) y ^ (2) / 5
   3y ^ 2 / 5x ^ 6
 Answer:
   3y ^ 2 / 5x ^ 6Note: answer is not between the options. Rewrite the expression again, or the options.

Answer 2

$\dfrac{-9x^{-1}y^{-1}}{-15x^5 y^{-3}}\ \ \ \text{assume}\ x\neq0\ \wedge\ y\neq0\\\\\text{Use:}\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\a^{-n}=\dfrac{1}{a^n}$

$\dfrac{-9x^{-1}y^{-1}}{-15x^5 y^{-3}}=\dfrac{-9:3}{-15:3}\cdot x^{-1-5}y^{-1-(-3)}=\dfrac{3}{5}\cdot x^{-6}y^{-1+3}\\\\=\dfrac{3}{5}\cdot\dfrac{1}{x^6}\cdot y^2=\boxed{\dfrac{3y^2}{5x^6}}$