Example 5: Exponent Laws

Exponents and Roots

Example 5

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

Problem

\text{In }3^{4}\cdot 3^{5}\text{, what is the exponent on }3?

1. Recognize Pattern

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

2. Apply Method

6^{4}\cdot 6^{3}=6^{7}=279936

3. Conclude

3^{4}\cdot 3^{5}=3^{9}

Final answer

3^{4}\cdot 3^{5}=3^{9}