Question

Simplify this expression

((a^8a^9)^1/7)/a^2

The lesson this is from covers rational exponents if that helps.

Answer 1

`\bf ~~~~~~~~~~~~\textit{negative exponents}\\\\ a^(-n) \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^(-n) \qquad \qquad a^n\implies \cfrac{1}{a^(-n)} \\\\\\ \textit{also recall that}\qquad a^{( n)/( m)} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{( n)/( m)}\\\\ -------------------------------\\\\`


`\bf \cfrac{(a^8a^9)^{(1)/(7)}}{a^2}\implies \cfrac{(a^(8+9))^{(1)/(7)}}{a^2}\implies \cfrac{(a^(17))^{(1)/(7)}}{a^2}\implies \cfrac{a^{17\cdot (1)/(7)}}{a^2}\implies \cfrac{a^{(17)/(7)}}{a^2} \\\\\\ \cfrac{a^{(17)/(7)}}{1}\cdot \cfrac{1}{a^2}\implies a^{(17)/(7)}\cdot a^(-2)\implies a^{(17)/(7)-2}\implies a^{(17-14)/(7)}\implies a^{(3)/(7)}\implies \sqrt[7]{a^3}`