Question

How to simplify (4x^-4y^2)^-3? The -4, 2 and -3 are the exponents.

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}\\\\ (4x^(-4)y^2)^(-3)\implies \cfrac{1}{(4x^(-4)y^2)^3}\implies \stackrel{\textit{distributing the exponent}}{\cfrac{1}{\left( 4^3x^(-4\cdot 3)y^(2\cdot 3) \right)}} \\\\\\ \cfrac{1}{64x^(-12)y^6}\implies \cfrac{x^(12)}{64y^6}`