Question

Simplify leaving your answer with positive exponents.

Answer 1

$\bf \left( \cfrac{5m^{\frac{4}{3}}}{n^{\frac{2}{3}}} \right)^{-\frac{2}{3}}\left(\cfrac{m^4}{8n^5} \right)^{-\frac{4}{3}}\implies \left( \cfrac{n^{\frac{2}{3}}}{5m^{\frac{4}{3}}} \right)^{\frac{2}{3}}\left(\cfrac{8n^5}{m^4} \right)^{\frac{4}{3}}\impliedby \begin{array}{llll} \textit{and now we}\\ \textit{distribute}\\ \textit{the exponent} \end{array}$

$\bf \left( \cfrac{n^{\frac{2}{3}\cdot \frac{2}{3}}}{5^{\frac{2}{3}}m^{\frac{4}{3}\cdot \frac{2}{3}}} \right)\left( \cfrac{8^{\frac{4}{3}}n^{5\cdot \frac{4}{3}}}{m^{4\cdot \frac{4}{3}}} \right)\implies \cfrac{n^{\frac{4}{9}}}{5^{\frac{2}{3}}m^{\frac{8}{9}}}\cdot \cfrac{8^{\frac{4}{3}}n^{\frac{20}{3}}}{m^{\frac{16}{3}}}\implies \cfrac{8^{\frac{4}{3}}n^{\frac{4}{9}+\frac{20}{3}}}{5^{\frac{2}{3}}m^{\frac{8}{9}+\frac{16}{3}}}$

$\bf \cfrac{8^{\frac{4}{3}}n^{\frac{4+60}{9}}}{5^{\frac{2}{3}}m^{\frac{8+48}{9}}}\implies \cfrac{8^{\frac{4}{3}}n^{\frac{64}{9}}}{5^{\frac{2}{3}}m^{\frac{56}{9}}}$