CPM Homework Help : CALC Problem 1-56

Wei Kit loves shortcuts! When calculating with fractional exponents, he looks for a way to avoid using his calculator. For example, he found out that $8^{2/3} = 4$ by using the method below:

$8 ^ { 2 / 3 } = ( \sqrt [ 3 ] { 8 } ) ^ { 2 } = ( 2 ) ^ { 2 } = 4$

Use Wei Kit's method to evaluate the following expressions:

$100^{3/2}$
Hint (a):
To avoid dealing with large numbers, find the square root of $100$ first. After all, $100^{ \frac{1}{2} }$ is equivalent to $\sqrt{100}$ .

$27^{4/3}$
Steps (b):
Step 1: What is the cube-root of $27$ ?
Step 2: Raise the cube-root of $27$ to the $4$ th-power.

$16^{3/4}$
Hint (c):
What is the fourth-root of $16$ ?

$9^{4/2}$
Hint (d):
Reduce $\frac{4}{2}$ before evaluating.