Simplify fifth root of 8xy^7* fifth root of 6x^6

$\sqrt[5]{8 x y^{7}} \cdot \sqrt[5]{6 x^{6}}$

Rewrite $8 x y^{7}$ as $y^{5} \cdot (8 x y^{2})$ .

Factor out $y^{5}$ .

$\sqrt[5]{8 x (y^{5} y^{2})} \cdot \sqrt[5]{6 x^{6}}$

Move $x$ .

$\sqrt[5]{8 y^{5} x y^{2}} \cdot \sqrt[5]{6 x^{6}}$

Reorder $8$ and $y^{5}$ .

$\sqrt[5]{y^{5} \cdot 8 x y^{2}} \cdot \sqrt[5]{6 x^{6}}$

Add parentheses.

$\sqrt[5]{y^{5} \cdot 8 (x y^{2})} \cdot \sqrt[5]{6 x^{6}}$

Add parentheses.

$\sqrt[5]{y^{5} \cdot (8 x y^{2})} \cdot \sqrt[5]{6 x^{6}}$

Pull terms out from under the radical.

$y \sqrt[5]{8 x y^{2}} \cdot \sqrt[5]{6 x^{6}}$

Rewrite $6 x^{6}$ as $x^{5} \cdot (6 x)$ .

Factor out $x^{5}$ .

$y \sqrt[5]{8 x y^{2}} \cdot \sqrt[5]{6 (x^{5} x)}$

Reorder $6$ and $x^{5}$ .

$y \sqrt[5]{8 x y^{2}} \cdot \sqrt[5]{x^{5} \cdot 6 x}$

Add parentheses.

$y \sqrt[5]{8 x y^{2}} \cdot \sqrt[5]{x^{5} \cdot (6 x)}$

Pull terms out from under the radical.

$y \sqrt[5]{8 x y^{2}} \cdot (x \sqrt[5]{6 x})$

Multiply $y \sqrt[5]{8 x y^{2}} (x \sqrt[5]{6 x})$ .

Combine using the product rule for radicals.

$y (x \sqrt[5]{8 x y^{2} (6 x)})$

Multiply $6$ by $8$ .

$y (x \sqrt[5]{48 x y^{2} x})$

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

$y (x \sqrt[5]{48 (x^{1} x) y^{2}})$

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

$y (x \sqrt[5]{48 (x^{1} x^{1}) y^{2}})$

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

$y (x \sqrt[5]{48 x^{1 + 1} y^{2}})$

Add $1$ and $1$ .

$y (x \sqrt[5]{48 x^{2} y^{2}})$

Reorder factors in $y (x \sqrt[5]{48 x^{2} y^{2}})$ .

$y x \sqrt[5]{48 x^{2} y^{2}}$