Question

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

Answer 1

`27^(-4/3)=1/81`

Explanation:

We have `27^(-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^(1/3)=(3^3)^(1/3)=3^(3xx(1/3))=3`

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

`3^4=81`

And lastly let's deal with the negative sign in the exponent:

`81^-1=1/81`

And so we can say that `27^(-4/3)=1/81`