Question

Simplify : (x^-2y^-4x^3)^-2

Answer 1

`\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^(-n) \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^(-n)} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^(-m)\implies a^(n-m) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (x^(-2)y^(-4)x^3)^(-2)\implies (x^(-2)x^3y^(-4))^(-2)\implies (x^(-2+3)y^(-4))^(-2)\implies (x^(1)y^(-4))^(-2) \\\\\\ \stackrel{\textit{distributing the exponent}~\hfill }{(x^(-2\cdot 1)y^(-2\cdot -4))\implies x^(-2)y^8}\implies \cfrac{1}{x^2}\cdot y^8\implies \cfrac{y^8}{x^2}`