Simplify -(-27)^(-4/3)

$- {(- 27)}^{- \frac{4}{3}}$

Step 1

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

$- \frac{1}{{(- 27)}^{\frac{4}{3}}}$

Step 2

Simplify the denominator.

Rewrite $- 27$ as ${(- 3)}^{3}$ .

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Raise $- 3$ to the power of $4$ .

$- \frac{1}{81}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{81}$

Decimal Form:

$- 0.01234567 \dots$