Example 10: Exponent Laws

Exponents and Roots

Example 10

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

Problem

\text{In }5^{3}\cdot 5^{1}\text{, what is the exponent on }5?

1. Recognize Pattern

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

2. Apply Method

5^{5}\cdot 5^{4}=5^{9}=1953125

3. Conclude

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

Final answer

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