Example 4: Exponent Laws

Exponents and Roots

Example 4

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

Problem

\text{In }3^{1}\cdot 3^{4}\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

4^{3}\cdot 4^{4}=4^{7}=16384

3. Conclude

3^{1}\cdot 3^{4}=3^{5}

Final answer

3^{1}\cdot 3^{4}=3^{5}