Question

Simplify the expression using the rules for 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}`

`\bf \cfrac{(a^(-3)b^(-1)c^(-5))^(-2)}{(a^5b^4c^2)^5}\implies \stackrel{\textit{distributing the exponent}}{\cfrac{(a^6b^2c^(10))}{(a^(25)b^(20)c^(10))}}\implies \cfrac{c^(10)c^(-10)}{a^(25)a^(-6)b^(20)b^(-2)} \\\\\\ \cfrac{c^(10-10)}{a^(25-6)b^(20-2)}\implies \cfrac{c^0}{a^(19)b^(18)}\implies \cfrac{1}{a^(19)b^(18)}`