Math Problem Statement
Bentuk sederhana dari \left( \frac{9a^2 b^{-1} c}{27a^3 b^2 c^2} \right)^{-1} adalah....
Solution
The given mathematical expression to simplify is:
Step 1: Simplify the fraction inside the parentheses
We begin by simplifying the fraction:
This can be broken down as follows:
- For the constants:
- For the powers of :
- For the powers of :
- For the powers of :
Thus, the fraction simplifies to:
Step 2: Apply the negative exponent
The expression now becomes:
Using the property of exponents, , the expression becomes:
Final Answer:
The simplified form is , which matches option A.
Let me know if you need more details or further clarification!
Here are 5 related questions for further practice:
- How do you simplify expressions with negative exponents?
- What is the rule for dividing terms with the same base but different exponents?
- How does multiplying by the reciprocal work when dealing with negative exponents?
- Can you simplify ?
- What happens when you apply a power of negative one to a fraction?
Tip: Always combine like terms (same base) by adding or subtracting exponents when multiplying or dividing powers.
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Math Problem Analysis
Mathematical Concepts
Algebra
Simplifying Fractions
Exponents
Formulas
Exponent rules: a^m / a^n = a^(m-n), (x^-1) = 1/x
Fraction simplification
Theorems
Properties of exponents
Simplification of algebraic expressions
Suitable Grade Level
Grades 10-12