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

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Answer 1 · 2017-01-27T12:08:29

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

We have $27^{- \frac{3}{4}}$ $27^(-3/4)$ . 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 $27 = 3^{3}$ $27=3^3$

Let's take the cube root first:

$27^{\frac{1}{3}} = {(3^{3})}^{\frac{1}{3}} = 3^{3 \times (\frac{1}{3})} = 3$ $27^(1/3)=(3^3)^(1/3)=3^(3xx(1/3))=3$

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

$3^{4} = 81$ $3^4=81$

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

$81^{- 1} = \frac{1}{81}$ $81^-1=1/81$

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

Simplify? 27−3427^(-3/4)