Example 12: Exponent Laws

Exponents and Roots

Example 12

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

Problem

\text{In }4^{3}\cdot 4^{4}\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

5^{5}\cdot 5^{1}=5^{6}=15625

3. Conclude

4^{3}\cdot 4^{4}=4^{7}

Final answer

4^{3}\cdot 4^{4}=4^{7}