Question

Simplify this expression

Answer 1

$\bf ~~~~~~~~~~~~\textit{negative exponents}\\\\ a^{-n} \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^{-n} \qquad \qquad a^n\implies \cfrac{1}{a^{-n}} \\\\\\ \textit{also recall that}\qquad a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\ -------------------------------$

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