Example 1: Exponent Laws

Exponents and Roots

Example 1

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

Problem

\text{In }2^{1}\cdot 2^{4}\text{, what is the exponent on }2?

1. Recognize Pattern

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

2. Apply Method

3^{3}\cdot 3^{2}=3^{5}=243

3. Conclude

2^{1}\cdot 2^{4}=2^{5}

Final answer

2^{1}\cdot 2^{4}=2^{5}