Simplify 8xy^3 cube root of 24x^11y^8

$8 x y^{3} \sqrt[3]{24 x^{11} y^{8}}$

Step 1

Rewrite $24 x^{11} y^{8}$ as ${(2 x^{3} y^{2})}^{3} \cdot (3 x^{2} y^{2})$ .

Factor $8$ out of $24$ .

$8 x y^{3} \sqrt[3]{8 (3) x^{11} y^{8}}$

Rewrite $8$ as $2^{3}$ .

$8 x y^{3} \sqrt[3]{2^{3} \cdot 3 x^{11} y^{8}}$

Factor out $x^{9}$ .

$8 x y^{3} \sqrt[3]{2^{3} \cdot 3 (x^{9} x^{2}) y^{8}}$

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

$8 x y^{3} \sqrt[3]{2^{3} \cdot 3 ({(x^{3})}^{3} x^{2}) y^{8}}$

Factor out $y^{6}$ .

$8 x y^{3} \sqrt[3]{2^{3} \cdot 3 ({(x^{3})}^{3} x^{2}) (y^{6} y^{2})}$

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

$8 x y^{3} \sqrt[3]{2^{3} \cdot 3 ({(x^{3})}^{3} x^{2}) ({(y^{2})}^{3} y^{2})}$

Move $x^{2}$ .

$8 x y^{3} \sqrt[3]{2^{3} \cdot 3 ({(x^{3})}^{3}) {(y^{2})}^{3} x^{2} y^{2}}$

Move $3$ .

$8 x y^{3} \sqrt[3]{(2^{3} ({(x^{3})}^{3})) {(y^{2})}^{3} \cdot 3 x^{2} y^{2}}$

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

$8 x y^{3} \sqrt[3]{{(2 x^{3} y^{2})}^{3} \cdot 3 x^{2} y^{2}}$

Add parentheses.

$8 x y^{3} \sqrt[3]{{(2 x^{3} y^{2})}^{3} \cdot 3 (x^{2} y^{2})}$

Add parentheses.

$8 x y^{3} \sqrt[3]{{(2 x^{3} y^{2})}^{3} \cdot (3 x^{2} y^{2})}$

Step 2

Pull terms out from under the radical.

$8 x y^{3} (2 x^{3} y^{2} \sqrt[3]{3 x^{2} y^{2}})$

Step 3

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

Move $x^{3}$ .

$8 (x^{3} x) y^{3} (2 y^{2} \sqrt[3]{3 x^{2} y^{2}})$

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

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

$8 (x^{3} x^{1}) y^{3} (2 y^{2} \sqrt[3]{3 x^{2} y^{2}})$

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

$8 x^{3 + 1} y^{3} (2 y^{2} \sqrt[3]{3 x^{2} y^{2}})$

Add $3$ and $1$ .

$8 x^{4} y^{3} (2 y^{2} \sqrt[3]{3 x^{2} y^{2}})$

Step 4

Multiply $y^{3}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$8 x^{4} (y^{2} y^{3}) (2 \sqrt[3]{3 x^{2} y^{2}})$

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

$8 x^{4} y^{2 + 3} (2 \sqrt[3]{3 x^{2} y^{2}})$

Add $2$ and $3$ .

$8 x^{4} y^{5} (2 \sqrt[3]{3 x^{2} y^{2}})$

Step 5

Multiply $2$ by $8$ .

$16 x^{4} y^{5} \sqrt[3]{3 x^{2} y^{2}}$

Simplify 8xy^3 cube root of 24x^11y^8

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