Home > APCALC > Chapter 1 > Lesson 1.2.3 > Problem1-56

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:

1. $100^{3/2}$

To avoid dealing with large numbers, find the square root of $100$ first.

$100^{ \frac{1}{2} }\text=\sqrt{100}.$

$100^{\frac{3}{2}}=\left (100^{\frac{1}{2}} \right )^3=$

$\left ( \sqrt{100} \right )^3=\underline{ \ \ \ \ \ \ \ \ \ \ }$

1. $27^{4/3}$

Step 1: What is the cube-root of $27$?

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

1. $16^{3/4}$

What is the fourth-root of $16$?

1. $9^{4/2}$

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