Math Problem Statement
Write (6x^5y^3)^2 / (3x^2y^7 × 4xy^-3) in the form ax^by^c where a, b, and c are integers.
Solution
The question provided asks to simplify the expression:
in the form , where , , and are integers.
Step-by-step solution:
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Expand the numerator:
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Expand the denominator:
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Divide the terms: Simplifying each factor:
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Final result:
Thus, the expression is simplified to .
Would you like further details or explanations on any step? Here are some related questions:
- How do you expand exponents like ?
- What are the rules for simplifying fractions with variables?
- How do you combine powers when multiplying terms with the same base?
- Why does dividing powers result in subtraction of exponents?
- What does the expression represent mathematically?
Tip: When simplifying algebraic expressions, always handle each variable separately using exponent rules.
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Math Problem Analysis
Mathematical Concepts
Algebra
Exponent Rules
Simplifying Expressions
Formulas
Power of a Power: (x^m)^n = x^(m*n)
Multiplying Powers: x^m * x^n = x^(m+n)
Dividing Powers: x^m / x^n = x^(m-n)
Theorems
Laws of Exponents
Suitable Grade Level
Grades 9-12