CPM Homework Help : CALC3RD Problem 1-56

Wei Kit loves patterns! When making calculations with rational exponents, he looks for a way to avoid using his calculator. For example, he knows 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.
$100^{ \frac{1}{2} }\text=\sqrt{100}.$
Steps (a):
$100^{\frac{3}{2}}=\left (100^{\frac{1}{2}} \right )^3=$
$\left ( \sqrt{100} \right )^3=\underline{ \ \ \ \ \ \ \ \ \ \ }$

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

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

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