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

1 Answer

Answer:

#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#