Algebra Examples

${(- 64)}^{- \frac{1}{3}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(- 64)}^{\frac{1}{3}}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Rewrite $- 64$ as ${(- 4)}^{3}$ .

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

Step 2.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 2.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.3.1

Cancel the common factor.

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

Step 2.3.2

Rewrite the expression.

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

Step 2.4

Evaluate the exponent.

$\frac{1}{- 4}$

Step 3

Move the negative in front of the fraction.

$- \frac{1}{4}$