Simplify -2 cube root of 5x*3 cube root of 25x^2

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

Step 1

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

Multiply $3$ by $- 2$ .

$- 6 \sqrt[3]{5 x} \sqrt[3]{25 x^{2}}$

Combine using the product rule for radicals.

$- 6 \sqrt[3]{25 x^{2} (5 x)}$

Multiply $5$ by $25$ .

$- 6 \sqrt[3]{125 x^{2} x}$

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

$- 6 \sqrt[3]{125 (x^{1} x^{2})}$

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

$- 6 \sqrt[3]{125 x^{1 + 2}}$

Add $1$ and $2$ .

$- 6 \sqrt[3]{125 x^{3}}$

Step 2

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

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

Step 3

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

$- 6 (5 x)$

Step 4

Multiply $5$ by $- 6$ .

$- 30 x$