Simplify the Radical Expression cube root of 5x* cube root of 25x^2

$\sqrt[3]{5 x} \cdot \sqrt[3]{25 x^{2}}$

Step 1

Multiply $\sqrt[3]{5 x} \sqrt[3]{25 x^{2}}$ .

Combine using the product rule for radicals.

$\sqrt[3]{5 x (25 x^{2})}$

Multiply $25$ by $5$ .

$\sqrt[3]{125 x \cdot x^{2}}$

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

Move $x^{2}$ .

$\sqrt[3]{125 (x^{2} x)}$

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

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

$\sqrt[3]{125 (x^{2} x^{1})}$

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

$\sqrt[3]{125 x^{2 + 1}}$

Add $2$ and $1$ .

$\sqrt[3]{125 x^{3}}$

Step 2

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

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

Step 3

Pull terms out from under the radical.

$5 x$