Example 7: Exponent Laws

Exponents and Roots

Example 7

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

Problem

\text{In }7^{4}\cdot 7^{2}\text{, what is the exponent on }7?

1. Recognize Pattern

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

2. Apply Method

2^{2}\cdot 2^{4}=2^{6}=64

3. Conclude

7^{4}\cdot 7^{2}=7^{6}

Final answer

7^{4}\cdot 7^{2}=7^{6}