Question

Is this correct? Could someone explain this?

Answer 1

`\cfrac{512^{(1)/(3)}}{64^{(2)/(3)}}\implies \cfrac{(2^9)^{(1)/(3)}}{(2^6)^{(2)/(3)}}\implies \cfrac{2^3}{2^4}\implies \cfrac{1}{2^4\cdot 2^(-3)}\implies \cfrac{1}{2} \\\\[-0.35em] ~\dotfill\\\\ \boxed{A}\qquad \left( \cfrac{64^{(2)/(3)}}{512^{(1)/(3)}} \right)^(-1)\implies \left( \cfrac{512^{(1)/(3)}}{64^{(2)/(3)}} \right)^(+1)\implies \stackrel{from~above}{\cfrac{1}{2}} \\\\[-0.35em] ~\dotfill`

`\boxed{B}\qquad \left( 64^{(2)/(3)}* 512^{-(1)/(3)} \right)^(-1)\implies \left( \cfrac{64^{(2)/(3)}}{512^{(1)/(3)}} \right)^(-1)\implies \left( \cfrac{512^{(1)/(3)}}{64^{(2)/(3)}} \right)^(+1)\implies \stackrel{from~above}{\cfrac{1}{2}} \\\\[-0.35em] ~\dotfill\\\\ \boxed{C}\qquad \cfrac{64^{-(2)/(3)}}{512^{-(1)/(3)}}\implies \cfrac{512^{(1)/(3)}}{64^{(2)/(3)}}\implies\stackrel{from~above}{\cfrac{1}{2}}`

Answer 2

It’s hard to explain but your right I got a good grade I did something like that so yeah