Question

Rewrite the expression as a single power with a negative exponent

Answer 1

`~\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] ~\dotfill\\\\ \left(\cfrac{1}{3}\cdot \cfrac{1}{3}\cdot \cfrac{1}{3}\cdot \cfrac{1}{3} \right)^2\implies \left[ \left( \cfrac{1}{3} \right)^4 \right]^2\implies \left( \cfrac{1^4}{3^4} \right)^2 \\\\\\ \left( \cfrac{1^(4\cdot 2)}{3^(4\cdot 2)} \right) \implies \cfrac{1}{3^8} \implies 3^(-8)`

let's recall that

`\begin{array}{llll} 1^1&=&1\\ 1^(10)&=&1\\ 1^(1,000)&=&1\\ 1^(1,000,000,000)&=&1\\ 1^(1,000,000,000,000)&=&1\\ \end{array}`