Simplify the cube root How would one simplify the cube root of $x^{64}$? Please show the solution step by step if possible. Been a while since I took math so please forgive the simplicity of this question... Thank you in advance.
$\sqrt[3]{x^{64}}=\sqrt[3]{x^{21\cdot 3+1}}=x^{21}\sqrt[3]{x}$.
You need to be careful.  Assuming that $x$ is real, one has $x^{64}$ is always a non-negative real number, and the cube root of a non-negative real number will again be a non-negative real.

$\sqrt[3]{x^{64}}=|x|^{\frac{64}{3}}=|x^{21}\cdot \sqrt[3]{x}|$

Without such care, one can arrive at incorrect results such as $\sqrt{x^2}=x$, which would imply things such as $1=-1$ (by plugging in $-1$ in for $x$)