Simplify cube root of -49x* cube root of 7x^2

$\sqrt[3]{- 49 x} \cdot \sqrt[3]{7 x^{2}}$

Step 1

Rewrite $- 49 x$ as ${({(- 1)}^{3})}^{3} \cdot (49 x)$ .

Rewrite $- 49$ as $- 1 (49)$ .

$\sqrt[3]{- 1 (49) x} \cdot \sqrt[3]{7 x^{2}}$

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$\sqrt[3]{{(- 1)}^{3} \cdot 49 x} \cdot \sqrt[3]{7 x^{2}}$

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$\sqrt[3]{{({(- 1)}^{3})}^{3} \cdot 49 x} \cdot \sqrt[3]{7 x^{2}}$

Add parentheses.

$\sqrt[3]{{({(- 1)}^{3})}^{3} \cdot (49 x)} \cdot \sqrt[3]{7 x^{2}}$

Step 2

Pull terms out from under the radical.

${(- 1)}^{3} \sqrt[3]{49 x} \cdot \sqrt[3]{7 x^{2}}$

Step 3

Simplify the expression.

Raise $- 1$ to the power of $3$ .

$- 1 \sqrt[3]{49 x} \cdot \sqrt[3]{7 x^{2}}$

Rewrite $- 1 \sqrt[3]{49 x}$ as $- \sqrt[3]{49 x}$ .

$- \sqrt[3]{49 x} \cdot \sqrt[3]{7 x^{2}}$

Step 4

Multiply $- \sqrt[3]{49 x} \sqrt[3]{7 x^{2}}$ .

Combine using the product rule for radicals.

$- \sqrt[3]{7 x^{2} (49 x)}$

Multiply $49$ by $7$ .

$- \sqrt[3]{343 x^{2} x}$

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

$- \sqrt[3]{343 (x^{1} x^{2})}$

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

$- \sqrt[3]{343 x^{1 + 2}}$

Add $1$ and $2$ .

$- \sqrt[3]{343 x^{3}}$

Step 5

Rewrite $343 x^{3}$ as ${(7 x)}^{3}$ .

$- \sqrt[3]{{(7 x)}^{3}}$

Step 6

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

$- (7 x)$

Step 7

Multiply $7$ by $- 1$ .

$- 7 x$