Math Problem Statement
Simplify the expression \(\frac{(-2a^{-2}b^3c^{-3})^2}{(-3a^{-4}b^{-2}c^{-2})^2}\).
Solution
Let's simplify the given expression step by step.
Given expression:
Step 1: Apply the power rule
Each term inside the parentheses is squared:
Numerator:
Denominator:
Thus, the expression becomes:
Step 2: Simplify each base separately using
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For :
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For :
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For :
Thus, we get:
Step 3: Rewrite the final answer
Since is in the numerator, move it to the denominator:
Final Answer:
Would you like a more detailed breakdown of any step?
Here are five related questions to deepen your understanding:
- How do you simplify expressions with negative exponents?
- What is the general rule for distributing exponents over multiplication?
- How would the solution change if different exponents were used?
- What happens when the base inside parentheses is negative?
- How does exponentiation affect fraction simplification?
Tip: Always simplify exponents step by step and apply exponent rules carefully to avoid mistakes! 😊
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Math Problem Analysis
Mathematical Concepts
Algebra
Exponent Rules
Simplifying Expressions
Formulas
Power of a product rule: \((xy)^m = x^m y^m\)
Quotient of powers rule: \(\frac{x^m}{x^n} = x^{m-n}\)
Negative exponent rule: \(x^{-n} = \frac{1}{x^n}\)
Theorems
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Suitable Grade Level
Grades 8-10