### 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 82/3 = 4 by using the method below:

82/3 = $( \sqrt [ 3 ] { 8 } ) ^ { 2 }$ = (2)2 = 4

Use Wei Kit’s method to evaluate the following expressions: Homework Help ✎

1. 1003/2

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

$\text{Afterall, } 100^{ \frac{1}{2} }\text{ is equivalent to }\sqrt{100}.$

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

2. 274/3

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

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

3. 163/4

What is the fourth-root of 16?

4. 94/2

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