Simplify 24 root of s*s^8

$\sqrt[24]{s \cdot s^{8}}$

Multiply $s$ by $s^{8}$ by adding the exponents.

Multiply $s$ by $s^{8}$ .

Raise $s$ to the power of $1$ .

$\sqrt[24]{s^{1} s^{8}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[24]{s^{1 + 8}}$

Add $1$ and $8$ .

$\sqrt[24]{s^{9}}$

Rewrite $s^{9}$ as ${(s^{3})}^{3}$ .

$\sqrt[24]{{(s^{3})}^{3}}$

Rewrite $\sqrt[24]{{(s^{3})}^{3}}$ as $\sqrt[8]{\sqrt[3]{{(s^{3})}^{3}}}$ .

$\sqrt[8]{\sqrt[3]{{(s^{3})}^{3}}}$

Pull terms out from under the radical, assuming real numbers.

$\sqrt[8]{s^{3}}$