Question

Simplify the expression please

Answer 1

`\bf \left( a^{-(1)/(4)}\cdot b^2 \right)^{(5)/(4)}\impliedby \textit{first off, distribute the exponent} \\\\\\ a^{-(1)/(4)\cdot (5)/(4)}\cdot b^{2\cdot (5)/(4)}\implies a^{-(5)/(16)}\cdot b^{(5)/(2)}\implies a^{-(5)/(16)}\cdot b^{(40)/(16)}\implies \cfrac{b^{(40)/(16)}}{a^{(5)/(16)}} \\\\\\ \cfrac{\sqrt[16]{b^(40)}}{\sqrt[16]{a^5}}\implies \sqrt[16]{\cfrac{b^(40)}{a^5}}`

now.. not sure if that's really simplified per se, I guess is a little.

you could also just take some "b" from the root and rationalize the denominator and end up with
`\bf \cfrac{b^2\sqrt[16]{a^(11)b^8}}{a}`

then again, not sure how simplified per se that one is either.