Math Problem Statement
(a^2b^3)^2 / c^3 / a^3b^2c / a^-2
Solution
To simplify the expression:
we will follow the order of operations and apply the laws of exponents step by step.
Step 1: Simplify the powers
First, simplify :
Now, rewrite the expression with these simplified powers:
Step 2: Rewrite the division as multiplication
Division by a fraction is the same as multiplication by its reciprocal:
Step 3: Combine fractions
Combine the fractions by multiplying the numerators and the denominators:
Step 4: Simplify the exponents
Combine like terms by adding the exponents of the same bases:
Now, substitute these simplified exponents into the expression:
Step 5: Rewrite with positive exponents
To express the answer with positive exponents, rewrite negative exponents as reciprocals:
Conclusion
The simplified expression is:
Would you like more details or have any questions?
Related Questions:
- How do you simplify expressions with multiple variables and exponents?
- What are the rules of exponents, and how are they applied in algebraic expressions?
- How can expressions with negative exponents be rewritten with positive exponents?
- What is the importance of the order of operations in simplifying algebraic expressions?
- How do you simplify complex fractions involving multiple variables?
Tip: When dealing with exponents, remember that multiplying like bases involves adding their exponents, and dividing like bases involves subtracting their exponents.
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Math Problem Analysis
Mathematical Concepts
Exponents
Fractions
Order of Operations
Formulas
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Theorems
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Suitable Grade Level
High School