Example 11: Exponent Laws

Exponents and Roots

Example 11

Step-by-step worked example for this lesson track.

Problem

\text{In }4^{5}\cdot 4^{2}\text{, what is the exponent on }4?

1. Recognize Pattern

a^m\cdot a^n=a^{m+n},\;\frac{a^m}{a^n}=a^{m-n}

2. Apply Method

3^{2}\cdot 3^{1}=3^{3}=27

3. Conclude

4^{5}\cdot 4^{2}=4^{7}

Final answer

4^{5}\cdot 4^{2}=4^{7}