# How do you simplify  (27^-⅔)/(27^-½)?

May 7, 2016

This is easier than it appears at first, the bases are both 27.
Use one of the first laws of indices. "If you are dividing and the bases are the same, subtract the indices"

Notice that $\frac{2}{3}$ is a bigger fraction than $\frac{1}{2}$
Therefore subtracting in the numerator will give a negative answer, which will need further attention, We can subtract in the denominator rather.

1/27^(-1/2 - (-2)/3 = 1/27^(-1/2 + 2/3 $\text{ } - \frac{1}{2} + \frac{2}{3}$
$\text{ } = \frac{- 3 + 4}{6}$
=$\frac{1}{27} ^ \left(\frac{1}{6}\right)$

=$\frac{1}{{3}^{3}} ^ \left(\frac{1}{6}\right)$

=1/(3^(1/2) = $\frac{1}{\sqrt{3}}$