Simplify cube root of 125x^12* square root of 121x^3

$\sqrt[3]{125 x^{12}} \cdot \sqrt{121 x^{3}}$

Step 1

Rewrite $125 x^{12}$ as ${(5 x^{4})}^{3}$ .

$\sqrt[3]{{(5 x^{4})}^{3}} \cdot \sqrt{121 x^{3}}$

Step 2

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

$5 x^{4} \cdot \sqrt{121 x^{3}}$

Step 3

Rewrite $121 x^{3}$ as ${(11 x)}^{2} x$ .

Rewrite $121$ as $11^{2}$ .

$5 x^{4} \cdot \sqrt{11^{2} x^{3}}$

Factor out $x^{2}$ .

$5 x^{4} \cdot \sqrt{11^{2} (x^{2} x)}$

Rewrite $11^{2} x^{2}$ as ${(11 x)}^{2}$ .

$5 x^{4} \cdot \sqrt{{(11 x)}^{2} x}$

Step 4

Pull terms out from under the radical.

$5 x^{4} \cdot (11 x \sqrt{x})$

Step 5

Multiply $x^{4}$ by $x$ by adding the exponents.

Move $x$ .

$5 (x \cdot x^{4}) \cdot (11 \sqrt{x})$

Multiply $x$ by $x^{4}$ .

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

$5 (x^{1} x^{4}) \cdot (11 \sqrt{x})$

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

$5 x^{1 + 4} \cdot (11 \sqrt{x})$

Add $1$ and $4$ .

$5 x^{5} \cdot (11 \sqrt{x})$

Step 6

Multiply $11$ by $5$ .

$55 x^{5} \sqrt{x}$