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what the power a when 5^a = 1/125

Sagot :

Space

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

  1. Rewrite:                                                                                                                [tex]\displaystyle 5^a = \frac{1}{5^3}[/tex]
  2. Rewrite [Exponential Property - Rewrite]:                                                       [tex]\displaystyle 5^a = 5^{-3}[/tex]
  3. Set:                                                                                                                    [tex]\displaystyle a = -3[/tex]
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