Evaluate ( cube root of 2)/( cube root of 54)

$\frac{\sqrt[3]{2}}{\sqrt[3]{54}}$

Step 1

Combine $\sqrt[3]{2}$ and $\sqrt[3]{54}$ into a single radical.

$\sqrt[3]{\frac{2}{54}}$

Step 2

Cancel the common factor of $2$ and $54$ .

Factor $2$ out of $2$ .

$\sqrt[3]{\frac{2 (1)}{54}}$

Cancel the common factors.

Factor $2$ out of $54$ .

$\sqrt[3]{\frac{2 \cdot 1}{2 \cdot 27}}$

Cancel the common factor.

$\sqrt[3]{\frac{2 \cdot 1}{2 \cdot 27}}$

Rewrite the expression.

$\sqrt[3]{\frac{1}{27}}$

Step 3

Rewrite $\sqrt[3]{\frac{1}{27}}$ as $\frac{\sqrt[3]{1}}{\sqrt[3]{27}}$ .

$\frac{\sqrt[3]{1}}{\sqrt[3]{27}}$

Step 4

Any root of $1$ is $1$ .

$\frac{1}{\sqrt[3]{27}}$

Step 5

Simplify the denominator.

Rewrite $27$ as $3^{3}$ .

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

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

$\frac{1}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$