### Home > CALC > Chapter 1 > Lesson 1.2.3 > Problem1-56

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:

1. $100^{3/2}$

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

1. $27^{4/3}$

Step 1: What is the cube-root of $27$?
Step 2: Raise the cube-root of $27$ to the $4$th-power.

1. $16^{3/4}$

What is the fourth-root of $16$?

1. $9^{4/2}$

Reduce $\frac{4}{2}$ before evaluating.