Answer:
[tex]\displaystyle (8a^{-3})^\Bigg{\frac{-2}{3}} = \frac{a^{2}}{4}[/tex]
General Formulas and Concepts:
Algebra I
- Exponential Property [Powering]:
[tex]\displaystyle (b^m)^n = b^{m \cdot n}[/tex] - Exponential Property [Rewrite]:
[tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]
Step-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle (8a^{-3})^\Bigg{\frac{-2}{3}}[/tex]
Step 2: Simplify
- [Expression] Expand [Exponential Property - Powering]:
[tex]\displaystyle (8a^{-3})^\Bigg{\frac{-2}{3}} = 8^\Bigg{\frac{-2}{3}} \Bigg( a^\Bigg{\frac{-3(-2)}{3}} \Bigg)[/tex] - Evaluate exponents:
[tex]\displaystyle (8a^{-3})^\Bigg{\frac{-2}{3}} = \frac{a^{2}}{4}[/tex]
∴ we have simplified the given expression.
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Learn more about Algebra I: https://brainly.com/question/15985602
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Topic: Algebra I
