Question

I NEED HELP ON THIS EQUATION PLEASE. Simplify the radical expression so that you can be written as k h^r s^t

Answer 1

`\cfrac{\sqrt[5]{1024h^(-8)s^5}}{\sqrt[5]{h^(-5)s^9}}\implies \sqrt[5]{\cfrac{1024h^(-8)s^5}{h^(-5)s^9}}\implies \left( \cfrac{2^(10)h^(-8)s^5}{h^(-5)s^9} \right)^{(1)/(5)}\implies \left( \cfrac{2^(10)}{h^(-5)h^8s^(-5)s^9} \right)^{(1)/(5)}`

`\left( \cfrac{2^(10)}{h^(8-5)s^(9-5)} \right)^{(1)/(5)}\implies \left( \cfrac{2^(10)}{h^3 s^4} \right)^{(1)/(5)}\implies \cfrac{2^{10\cdot (1)/(5)}}{h^{3\cdot (1)/(5)}s^{4\cdot (1)/(5)}} \\\\\\ \cfrac{2^2}{h^{(3)/(5)}s^{(4)/(5)}}\implies {\Large \begin{array}{llll} \stackrel{k ~ ~~ ~ r ~~~ t }{4h^{-(3)/(5)}s^{-(4)/(5)}} \end{array}}`