Evaluate 1/4-2 cube root of -1/216

$\frac{1}{4} - 2 \sqrt[3]{- \frac{1}{216}}$

Simplify each term.

Rewrite $- \frac{1}{216}$ as ${(- \frac{1}{6})}^{3}$ .

$\frac{1}{4} - 2 \sqrt[3]{{(- \frac{1}{6})}^{3}}$

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

$\frac{1}{4} - 2 (- \frac{1}{6})$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$\frac{1}{4} - 2 (\frac{- 1}{6})$

Factor $2$ out of $- 2$ .

$\frac{1}{4} + 2 (- 1) \frac{- 1}{6}$

Factor $2$ out of $6$ .

$\frac{1}{4} + 2 \cdot - 1 \frac{- 1}{2 \cdot 3}$

Cancel the common factor.

$\frac{1}{4} + 2 \cdot - 1 \frac{- 1}{2 \cdot 3}$

Rewrite the expression.

$\frac{1}{4} - 1 (\frac{- 1}{3})$

Move the negative in front of the fraction.

$\frac{1}{4} - 1 (- \frac{1}{3})$

Multiply $- 1 (- \frac{1}{3})$ .

Multiply $- 1$ by $- 1$ .

$\frac{1}{4} + 1 (\frac{1}{3})$

Multiply $\frac{1}{3}$ by $1$ .

$\frac{1}{4} + \frac{1}{3}$

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{4} \cdot \frac{3}{3} + \frac{1}{3}$

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{4} \cdot \frac{3}{3} + \frac{1}{3} \cdot \frac{4}{4}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$\frac{3}{4 \cdot 3} + \frac{1}{3} \cdot \frac{4}{4}$

Multiply $4$ by $3$ .

$\frac{3}{12} + \frac{1}{3} \cdot \frac{4}{4}$

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$\frac{3}{12} + \frac{4}{3 \cdot 4}$

Multiply $3$ by $4$ .

$\frac{3}{12} + \frac{4}{12}$

Combine the numerators over the common denominator.

$\frac{3 + 4}{12}$

Add $3$ and $4$ .

$\frac{7}{12}$

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{12}$

Decimal Form:

$0.58\overline{3}$

Evaluate 1/4-2 cube root of -1/216

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