Question

Simplify the expression (5x^2y^-5)^-3

Answer 1

y^15/125x^6

Explanation:

Answer 2

`\large\boxed{(1)/(125)x^(-6)y^(15)=(x^(-6)y^(15))/(125)=(y^(15))/(125x^6)}`

Explanation:

`\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)=(1)/(a^n)\\\\\bigg(5x^2y^(-5)\bigg)^(-3)=5^(-3)\cdot(x^2)^(-3)\cdot(y^(-5))^(-3)\qquad(1)\\\\=(1)/(5^3)\cdot x^(2\cdot(-3))\cdot y^((-5)(-3))\qquad(3)\&(2)\\\\=(1)/(125)\cdot x^(-6)\cdot y^(15)\\\\=(1)/(125)\cdot(1)/(x^6)\cdot y^(15)\qquad(3)\\\\=(y^(15))/(125x^6)`