Question

Solve
$y^6=512$

Answer 1

$y^6=512$

Factors of $512=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$

$y^6=2^9$

$\Rightarrow y={\left(2^9\right)}^{\frac{1}{6}}$

$\therefore y=2^{9\times \frac{1}{6}}=2^{\frac{3}{2}}=\sqrt{8}=2\sqrt{2}$

$\therefore y=2\sqrt{2}$