Simplify square root of s^7 fifth root of s^7

$\sqrt{s^{7}} \sqrt[5]{s^{7}}$

Rewrite $s^{7}$ as ${(s^{3})}^{2} s$ .

Factor out $s^{6}$ .

$\sqrt{s^{6} s} \sqrt[5]{s^{7}}$

Rewrite $s^{6}$ as ${(s^{3})}^{2}$ .

$\sqrt{{(s^{3})}^{2} s} \sqrt[5]{s^{7}}$

Pull terms out from under the radical.

$s^{3} \sqrt{s} \sqrt[5]{s^{7}}$

Factor out $s^{5}$ .

$s^{3} \sqrt{s} \sqrt[5]{s^{5} s^{2}}$

Pull terms out from under the radical.

$s^{3} \sqrt{s} (s \sqrt[5]{s^{2}})$

Multiply $s^{3}$ by $s$ by adding the exponents.

Move $s$ .

$s \cdot s^{3} \sqrt{s} \sqrt[5]{s^{2}}$

Multiply $s$ by $s^{3}$ .

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

$s^{1} s^{3} \sqrt{s} \sqrt[5]{s^{2}}$

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

$s^{1 + 3} \sqrt{s} \sqrt[5]{s^{2}}$

Add $1$ and $3$ .

$s^{4} \sqrt{s} \sqrt[5]{s^{2}}$

Multiply $s^{4} \sqrt{s} \sqrt[5]{s^{2}}$ .

Rewrite the expression using the least common index of $10$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{s^{2}}$ as $s^{\frac{2}{5}}$ .

$s^{4} (s^{\frac{2}{5}} \sqrt{s})$

Rewrite $s^{\frac{2}{5}}$ as $s^{\frac{4}{10}}$ .

$s^{4} (s^{\frac{4}{10}} \sqrt{s})$

Rewrite $s^{\frac{4}{10}}$ as $\sqrt[10]{s^{4}}$ .

$s^{4} (\sqrt[10]{s^{4}} \sqrt{s})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{s}$ as $s^{\frac{1}{2}}$ .

$s^{4} (\sqrt[10]{s^{4}} s^{\frac{1}{2}})$

Rewrite $s^{\frac{1}{2}}$ as $s^{\frac{5}{10}}$ .

$s^{4} (\sqrt[10]{s^{4}} s^{\frac{5}{10}})$

Rewrite $s^{\frac{5}{10}}$ as $\sqrt[10]{s^{5}}$ .

$s^{4} (\sqrt[10]{s^{4}} \sqrt[10]{s^{5}})$

Combine using the product rule for radicals.

$s^{4} \sqrt[10]{s^{4} s^{5}}$

Multiply $s^{4}$ by $s^{5}$ by adding the exponents.

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

$s^{4} \sqrt[10]{s^{4 + 5}}$

Add $4$ and $5$ .

$s^{4} \sqrt[10]{s^{9}}$