Math Problem Statement
Simplify
Simplify \left( \frac{2a^{-2}}{b^{-3}} \right)^{-3}
Solution
The expression in the image is:
To simplify, let's break it down step by step:
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Apply the exponent to the fraction and each term inside:
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Simplify each part:
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Substitute back into the fraction:
Thus, the simplified expression is:
Would you like more clarification or have additional questions?
Here are some related questions to explore further:
- How do negative exponents affect the simplification process?
- What is the significance of a negative exponent in a fraction?
- How do we handle exponents when simplifying fractions in algebra?
- Can we apply similar steps to simplify expressions with more complex powers or variables?
- What role does the distributive property play when dealing with exponents?
Tip: Remember that when raising a fraction to a power, you apply the exponent to both the numerator and denominator individually!
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Math Problem Analysis
Mathematical Concepts
Algebra
Exponents and Powers
Fractional Exponents
Formulas
Power of a quotient: (a/b)^m = a^m / b^m
Negative exponent rule: a^{-m} = 1 / a^m
Product of exponents: (a^m)^n = a^{m*n}
Theorems
Exponentiation rules
Suitable Grade Level
Grades 8-10