Simplify cube root of -3*(1/375)^(1/3)

$\sqrt[3]{- 3} \cdot {(\frac{1}{375})}^{\frac{1}{3}}$

Step 1

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

Rewrite $- 3$ as $- 1 (3)$ .

$\sqrt[3]{- 1 (3)} \cdot {(\frac{1}{375})}^{\frac{1}{3}}$

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

$\sqrt[3]{{(- 1)}^{3} \cdot 3} \cdot {(\frac{1}{375})}^{\frac{1}{3}}$

Step 2

Pull terms out from under the radical.

$- 1 \sqrt[3]{3} \cdot {(\frac{1}{375})}^{\frac{1}{3}}$

Step 3

Simplify the expression.

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

$- \sqrt[3]{3} \cdot {(\frac{1}{375})}^{\frac{1}{3}}$

Apply the product rule to $\frac{1}{375}$ .

$- \sqrt[3]{3} \cdot \frac{1^{\frac{1}{3}}}{375^{\frac{1}{3}}}$

One to any power is one.

$- \sqrt[3]{3} \cdot \frac{1}{375^{\frac{1}{3}}}$

Step 4

Combine $\frac{1}{375^{\frac{1}{3}}}$ and $\sqrt[3]{3}$ .

$- \frac{\sqrt[3]{3}}{375^{\frac{1}{3}}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt[3]{3}}{375^{\frac{1}{3}}}$

Decimal Form:

$- 0.2$