Answer
$-\dfrac{1}{81}$
Work Step by Step
We want to break down this problem a little to be able to work with it. The number $-27$ can be broken down into a small base raised to a power: $(-3)^3$. Let us rewrite this number:
$-(-3^3)^{-4/3}$
Raising a power to a power means we can multiply the two powers or exponents together:
$-\left(-3^{(3)(-4/3)}\right)$
Multiply to simplify:
$-(-3^{-12/3})$
Reduce the fraction in the exponent by dividing both numerator and denominator by the greatest common factor, which is $3$, in this case:
$-(-3^{-4})$
We don't like to leave negative exponents. To get rid of the negative exponent, we change it into a positive exponent and use its reciprocal, meaning we take the reciprocal of its positive exponent:
$-\dfrac{1}{(-3^{4})}$
Use the rule $a^{-m}=\frac{1}{a^m}$ to obtain:
$=-\dfrac{1}{(-3)^4}=-\dfrac{1}{81}$
