Answer:
[tex]\large\boxed{\dfrac{1}{125}x^{-6}y^{15}=\dfrac{x^{-6}y^{15}}{125}=\dfrac{y^{15}}{125x^6}}[/tex]
Step-by-step explanation:
[tex]\bigg(5x^2y^{-5}\bigg)^{-3}\\\\\text{use}\\(1)\qquad(a\cdot b)^n=a^n\cdot b^n\\(2)\qquad(a^n)^m=a^{n\cdot m}\\(3)\qquad a^{-n}=\dfrac{1}{a^n}\\\\\bigg(5x^2y^{-5}\bigg)^{-3}=5^{-3}\cdot(x^2)^{-3}\cdot(y^{-5})^{-3}\qquad(1)\\\\=\dfrac{1}{5^3}\cdot x^{2\cdot(-3)}\cdot y^{(-5)(-3)}\qquad(3)\&(2)\\\\=\dfrac{1}{125}\cdot x^{-6}\cdot y^{15}\\\\=\dfrac{1}{125}\cdot\dfrac{1}{x^6}\cdot y^{15}\qquad(3)\\\\=\dfrac{y^{15}}{125x^6}[/tex]
