Simplify xy cube root of 54x^7y^10

$x y \sqrt[3]{54 x^{7} y^{10}}$

Step 1

Rewrite $54 x^{7} y^{10}$ as ${(3 x^{2} y^{3})}^{3} \cdot (2 x y)$ .

Factor $27$ out of $54$ .

$x y \sqrt[3]{27 (2) x^{7} y^{10}}$

Rewrite $27$ as $3^{3}$ .

$x y \sqrt[3]{3^{3} \cdot 2 x^{7} y^{10}}$

Factor out $x^{6}$ .

$x y \sqrt[3]{3^{3} \cdot 2 (x^{6} x) y^{10}}$

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

$x y \sqrt[3]{3^{3} \cdot 2 ({(x^{2})}^{3} x) y^{10}}$

Factor out $y^{9}$ .

$x y \sqrt[3]{3^{3} \cdot 2 ({(x^{2})}^{3} x) (y^{9} y)}$

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

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

Move $x$ .

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

Move $2$ .

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

Rewrite $(3^{3} ({(x^{2})}^{3})) {(y^{3})}^{3}$ as ${(3 x^{2} y^{3})}^{3}$ .

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

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

Multiply $x^{2}$ by $x$ .

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

$3 (x^{2} x^{1}) y (y^{3} \sqrt[3]{2 x y})$

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

$3 x^{2 + 1} y (y^{3} \sqrt[3]{2 x y})$

Add $2$ and $1$ .

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

Step 5

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

Move $y^{3}$ .

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

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

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

$3 x^{3} (y^{3} y^{1}) \sqrt[3]{2 x y}$

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

$3 x^{3} y^{3 + 1} \sqrt[3]{2 x y}$

Add $3$ and $1$ .

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

Simplify xy cube root of 54x^7y^10

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