CPM Homework Help : PC Problem 1-102

Add the rules from the Math Notes box to your Tool Kit. It does not matter how you “break up” the fractional exponent. To evaluate fractional exponents without a calculator, make the numbers small as soon as you can by taking the root first and then raising to the power.

Evaluate.

$64^{2/3} = (64^{1/3})^{2} = ?$
Hint (a):
Take the cube root of $64$ first. Then square your answer.

$125^{4/3} = \left(125^{1/3}\right)^{4} = ?$
Hint (b):
Follow the hint in (a).

$81^{3/4} = ?$
Answer (c):
$27$

$(\frac{27}{8})^{-2/3}=?$
Hint (d):
Flip the fraction first to eliminate the negative exponent. Then take the root first before doing the power.
Answer (d):
$\frac{4}{9}$