Evaluate $64 ^ { - 4 / 3 }$ without using a calculator.
A) $\frac { 1 } { 512 }$
B)64
C) $\frac { 1 } { 64 }$
D) $\frac { 1 } { 256 }$
E)256

Question

Quizplus · Accepted Answer

First we will write $64 ^ { - 4 / 3 }$ in the form of $\frac{1}{64^{4/3}}$.

Now, we know that $64 = 4^3$, so we can rewrite this as $\frac{1}{(4^3)^{4/3}}$.

Using the exponent rule of $(a^b)^c = a^{bc}$, we simplify to get $\frac{1}{4^{4}}$.

Therefore, $64 ^ { - 4 / 3 } = \frac { 1 } { 256 }$.

Evaluate 64−4/364 ^ { - 4 / 3 }64−4/3 Without Using a Calculator