Question

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

Answer 1

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