Math Problem Statement
Multiply and simplify the expression (8a^3b / b^5) * (5b / 4a^2).
Solution
The given problem is to multiply and simplify the following expression:
Step-by-Step Solution:
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Combine the two fractions: Multiply the numerators and denominators:
Simplify the numerator and denominator:
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Simplify the coefficients: Divide by :
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Simplify the variables:
- For , subtract the exponents: .
- For , subtract the exponents: .
The simplified expression becomes:
Final Answer:
Let me know if you'd like further clarification!
Here are 5 related questions to expand your understanding:
- How do you handle negative exponents in simplification?
- What happens if one term in the numerator or denominator equals zero?
- How do you multiply fractions with multiple variables?
- What are some tips for identifying like terms when simplifying expressions?
- How do you simplify expressions that involve roots instead of exponents?
Tip: When simplifying fractions, always handle coefficients and variables separately to avoid confusion.
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Math Problem Analysis
Mathematical Concepts
Algebra
Exponents
Fractions
Formulas
Exponent rules: a^m / a^n = a^(m-n)
Multiplication of fractions: (a/b) * (c/d) = (a*c) / (b*d)
Theorems
Exponent subtraction rule
Suitable Grade Level
Grades 8-10