# Simplify? 27^(-3/4)

${27}^{- \frac{4}{3}} = \frac{1}{81}$

#### Explanation:

We have ${27}^{- \frac{3}{4}}$. Let's talk about that power for a moment.

There are three things it's asking us to do:

• the numerator (4) is asking us to take the base number to that power

• the denominator (3) is asking us to take the nth root of the base number

• and lastly, because the power is negative, we are to put the base number into a fraction as the denominator (with 1 as the numerator)

This all becomes a little easier by seeing that $27 = {3}^{3}$

Let's take the cube root first:

${27}^{\frac{1}{3}} = {\left({3}^{3}\right)}^{\frac{1}{3}} = {3}^{3 \times \left(\frac{1}{3}\right)} = 3$

Now let's take that to the 4th power:

${3}^{4} = 81$

${81}^{-} 1 = \frac{1}{81}$
And so we can say that ${27}^{- \frac{4}{3}} = \frac{1}{81}$