Answer:
a = -3
General Formulas and Concepts:
Algebra I
- Solving Exponential Equations
- Exponential Property [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle 5^a = \frac{1}{125}[/tex]
Step 2: Solve for a
- Rewrite: [tex]\displaystyle 5^a = \frac{1}{5^3}[/tex]
- Rewrite [Exponential Property - Rewrite]: [tex]\displaystyle 5^a = 5^{-3}[/tex]
- Set: [tex]\displaystyle a = -3[/tex]
