Simplify 6xy^3 cube root of 135x^10y^9

$6 x y^{3} \sqrt[3]{135 x^{10} y^{9}}$

Step 1

Rewrite $135 x^{10} y^{9}$ as ${(3 x^{3} y^{3})}^{3} \cdot (5 x)$ .

Factor $27$ out of $135$ .

$6 x y^{3} \sqrt[3]{27 (5) x^{10} y^{9}}$

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

$6 x y^{3} \sqrt[3]{3^{3} \cdot 5 x^{10} y^{9}}$

Factor out $x^{9}$ .

$6 x y^{3} \sqrt[3]{3^{3} \cdot 5 (x^{9} x) y^{9}}$

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

$6 x y^{3} \sqrt[3]{3^{3} \cdot 5 ({(x^{3})}^{3} x) y^{9}}$

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

$6 x y^{3} \sqrt[3]{3^{3} \cdot 5 ({(x^{3})}^{3} x) {(y^{3})}^{3}}$

Move $x$ .

$6 x y^{3} \sqrt[3]{3^{3} \cdot 5 ({(x^{3})}^{3}) {(y^{3})}^{3} x}$

Move $5$ .

$6 x y^{3} \sqrt[3]{(3^{3} ({(x^{3})}^{3})) {(y^{3})}^{3} \cdot 5 x}$

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

$6 x y^{3} \sqrt[3]{{(3 x^{3} y^{3})}^{3} \cdot 5 x}$

Add parentheses.

$6 x y^{3} \sqrt[3]{{(3 x^{3} y^{3})}^{3} \cdot (5 x)}$

Step 2

Pull terms out from under the radical.

$6 x y^{3} (3 x^{3} y^{3} \sqrt[3]{5 x})$

Step 3

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

Move $x^{3}$ .

$6 (x^{3} x) y^{3} (3 y^{3} \sqrt[3]{5 x})$

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

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

$6 (x^{3} x^{1}) y^{3} (3 y^{3} \sqrt[3]{5 x})$

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

$6 x^{3 + 1} y^{3} (3 y^{3} \sqrt[3]{5 x})$

Add $3$ and $1$ .

$6 x^{4} y^{3} (3 y^{3} \sqrt[3]{5 x})$

Step 4

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

Move $y^{3}$ .

$6 x^{4} (y^{3} y^{3}) (3 \sqrt[3]{5 x})$

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

$6 x^{4} y^{3 + 3} (3 \sqrt[3]{5 x})$

Add $3$ and $3$ .

$6 x^{4} y^{6} (3 \sqrt[3]{5 x})$

Step 5

Multiply $3$ by $6$ .

$18 x^{4} y^{6} \sqrt[3]{5 x}$

Simplify 6xy^3 cube root of 135x^10y^9

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