Simplify 5x^3y^3 cube root of 8x^9y^6

$5 x^{3} y^{3} \sqrt[3]{8 x^{9} y^{6}}$

Step 1

Rewrite $8 x^{9} y^{6}$ as ${(2 x^{3} y^{2})}^{3}$ .

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

Step 2

Pull terms out from under the radical, assuming real numbers.

$5 x^{3} y^{3} (2 x^{3} y^{2})$

Step 3

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

Move $x^{3}$ .

$5 (x^{3} x^{3}) y^{3} (2 y^{2})$

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

$5 x^{3 + 3} y^{3} (2 y^{2})$

Add $3$ and $3$ .

$5 x^{6} y^{3} (2 y^{2})$

Step 4

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

Move $y^{2}$ .

$5 x^{6} (y^{2} y^{3}) \cdot 2$

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

$5 x^{6} y^{2 + 3} \cdot 2$

Add $2$ and $3$ .

$5 x^{6} y^{5} \cdot 2$

Step 5

Multiply $2$ by $5$ .

$10 x^{6} y^{5}$