Example 8: Exponent Laws

Exponents and Roots

Example 8

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

Problem

\text{In }2^{3}\cdot 2^{5}\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

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

3. Conclude

2^{3}\cdot 2^{5}=2^{8}

Final answer

2^{3}\cdot 2^{5}=2^{8}