Simplify 3 fourth root of 4x^3* fourth root of 8xy^5

$3 \sqrt[4]{4 x^{3}} \cdot \sqrt[4]{8 x y^{5}}$

Step 1

Rewrite $8 x y^{5}$ as $y^{4} \cdot (8 x y)$ .

Factor out $y^{4}$ .

$3 \sqrt[4]{4 x^{3}} \cdot \sqrt[4]{8 x (y^{4} y)}$

Move $x$ .

$3 \sqrt[4]{4 x^{3}} \cdot \sqrt[4]{8 y^{4} x y}$

Reorder $8$ and $y^{4}$ .

$3 \sqrt[4]{4 x^{3}} \cdot \sqrt[4]{y^{4} \cdot 8 x y}$

Add parentheses.

$3 \sqrt[4]{4 x^{3}} \cdot \sqrt[4]{y^{4} \cdot 8 (x y)}$

Add parentheses.

$3 \sqrt[4]{4 x^{3}} \cdot \sqrt[4]{y^{4} \cdot (8 x y)}$

Step 2

Pull terms out from under the radical.

$3 \sqrt[4]{4 x^{3}} \cdot (y \sqrt[4]{8 x y})$

Step 3

Multiply $3 \sqrt[4]{4 x^{3}} (y \sqrt[4]{8 x y})$ .

Combine using the product rule for radicals.

$3 (y \sqrt[4]{4 x^{3} (8 x y)})$

Multiply $8$ by $4$ .

$3 (y \sqrt[4]{32 x^{3} (x y)})$

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

$3 (y \sqrt[4]{32 (x^{1} x^{3}) y})$

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

$3 (y \sqrt[4]{32 x^{1 + 3} y})$

Add $1$ and $3$ .

$3 (y \sqrt[4]{32 x^{4} y})$

Step 4

Rewrite $32 x^{4} y$ as ${(2 x)}^{4} \cdot (2 y)$ .

Factor $16$ out of $32$ .

$3 (y \sqrt[4]{16 (2) x^{4} y})$

Rewrite $16$ as $2^{4}$ .

$3 (y \sqrt[4]{2^{4} \cdot 2 x^{4} y})$

Move $2$ .

$3 (y \sqrt[4]{2^{4} x^{4} \cdot 2 y})$

Rewrite $2^{4} x^{4}$ as ${(2 x)}^{4}$ .

$3 (y \sqrt[4]{{(2 x)}^{4} \cdot 2 y})$

Add parentheses.

$3 (y \sqrt[4]{{(2 x)}^{4} \cdot (2 y)})$

Step 5

Pull terms out from under the radical.

$3 (y (2 x \sqrt[4]{2 y}))$

Step 6

Simplify the expression.

Rewrite using the commutative property of multiplication.

$3 (2 y (x \sqrt[4]{2 y}))$

Multiply $2$ by $3$ .

$6 (y (x \sqrt[4]{2 y}))$

Reorder factors in $6 y (x \sqrt[4]{2 y})$ .

$6 y x \sqrt[4]{2 y}$

Simplify 3 fourth root of 4x^3* fourth root of 8xy^5

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