Simplify the Radical Expression 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 $| s^{3} | \sqrt{s} (s \sqrt[5]{s^{2}})$ .

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

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

$| s^{3} | (s (s^{\frac{1}{2}} \sqrt[5]{s^{2}}))$

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

$| s^{3} | (s (s^{\frac{5}{10}} \sqrt[5]{s^{2}}))$

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

$| s^{3} | (s (\sqrt[10]{s^{5}} \sqrt[5]{s^{2}}))$

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

$| s^{3} | (s (\sqrt[10]{s^{5}} s^{\frac{2}{5}}))$

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

$| s^{3} | (s (\sqrt[10]{s^{5}} s^{\frac{4}{10}}))$

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

$| s^{3} | (s (\sqrt[10]{s^{5}} \sqrt[10]{s^{4}}))$

Combine using the product rule for radicals.

$| s^{3} | (s \sqrt[10]{s^{5} s^{4}})$

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

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

$| s^{3} | (s \sqrt[10]{s^{5 + 4}})$

Add $5$ and $4$ .

$| s^{3} | (s \sqrt[10]{s^{9}})$

Reorder factors in $| s^{3} | (s \sqrt[10]{s^{9}})$ .

$s | s^{3} | \sqrt[10]{s^{9}}$