Answer:
C. [tex]\frac{1}{64}[/tex]
Step-by-step explanation:
First, we can set up our expression as such
[tex]\frac{4^{-\frac{11}{3} } }{4^{-\frac{2}{3} } }[/tex]
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 [tex]-\frac{11}{3}[/tex] and [tex]-\frac{2}{3}[/tex]
This means that the power would be
[tex]-\frac{11}{3}-(-\frac{2}{3})\\\\-\frac{11}{3}+\frac{2}{3}\\\\-\frac{9}{3}[/tex]
Now we can put this power back on its base and then simplify.
[tex]4^{-\frac{9}{3} } \\\\4^{-3} \\\\\frac{1}{4^{3} } \\\\\frac{1}{64}[/tex]
