Question

Simplify
(4x^-2y^3 ÷ xy^-4)^-2

Answer 1

`\bf ~~~~~~~~~~~~\textit{negative exponents}\\\\ a^(-n) \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^(-n) \qquad \qquad a^n\implies \cfrac{1}{a^(-n)}\\\\ -------------------------------\\\\`


`\bf (4x^(-2)y^3 / xy^(-4))^(-2)\implies \left( \cfrac{4x^(-2)y^3}{xy^(-4)} \right)^(-2)\implies \left( \cfrac{xy^(-4)}{4x^(-2)y^3} \right)^(2) \\\\\\ \textit{then we distribute the exponent}\left( \cfrac{x^2y^(-4\cdot 2)}{4^2x^(-2\cdot 2)y^(3\cdot 2)} \right)\implies \cfrac{x^2y^(-8)}{16x^(-4)y^6} \\\\\\ \cfrac{x^2\cdot x^4}{16y^6\cdot y^8}\implies \cfrac{x^(2+4)}{16y^(6+8)}\implies \cfrac{x^6}{16y^(14)}`

Answer 2

(‌4x−2y^3x‌y−4)−2
=‌x6y^8/16y^6‌
=‌x^6y^2/16

Hope this helps:)