Question

Simplify the following expression.

Answer 1

C.
`(1)/(64)`

Explanation:

First, we can set up our expression as such

`\frac{4^{-(11)/(3) } }{4^{-(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
`-(11)/(3)` and
`-(2)/(3)`

This means that the power would be

`-(11)/(3)-(-(2)/(3))\\\\-(11)/(3)+(2)/(3)\\\\-(9)/(3)`

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

`4^{-(9)/(3) } \\\\4^(-3) \\\\(1)/(4^(3) ) \\\\(1)/(64)`