Question

Simplify the following expression.

Answer 1

Answer:

C. $\frac{1}{64}$

Step-by-step explanation:

First, we can set up our expression as such

$\frac{4^{-\frac{11}{3} } }{4^{-\frac{2}{3} } }$

When you divide two numbers with the same base and different powers, all you do is subtract the lower power from the upper.

In this case the powers are $-\frac{11}{3}$ and $-\frac{2}{3}$

This means that the power would be

$-\frac{11}{3}-(-\frac{2}{3})\\\\-\frac{11}{3}+\frac{2}{3}\\\\-\frac{9}{3}$

Now we can put this power back on its base and then simplify.

$4^{-\frac{9}{3} } \\\\4^{-3} \\\\\frac{1}{4^{3} } \\\\\frac{1}{64}$