Question

Simplify leaving your answer with positive exponents.

Answer 1

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


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


`\bf \cfrac{8^{(4)/(3)}n^{(4+60)/(9)}}{5^{(2)/(3)}m^{(8+48)/(9)}}\implies \cfrac{8^{(4)/(3)}n^{(64)/(9)}}{5^{(2)/(3)}m^{(56)/(9)}}`