Math Problem Statement
solve
Solution
To simplify the expression , let's proceed step by step.
Given:
Step 1: Apply the negative exponent rule
The rule states that . Applying this:
Step 2: Expand the positive exponent
Raise the fraction to the power of 3:
Using the power rule :
Thus:
Step 3: Simplify the expression
Now substitute back:
Simplify the fraction:
Final Answer:
Let me know if you'd like more explanation!
Related Questions:
- What happens if the exponent were instead of ?
- How do you simplify an expression with multiple variables and exponents?
- What are the laws of exponents, and how are they applied to fractions?
- How does the negative exponent rule affect the structure of a fraction?
- Can you provide examples of real-world applications of exponent rules?
Tip:
When dealing with negative exponents, always remember to reciprocate the base and apply the positive power afterward!
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Math Problem Analysis
Mathematical Concepts
Exponents
Fractions
Algebra
Formulas
Negative exponent rule: \( a^{-b} = \frac{1}{a^b} \)
Power rule: \( (a^m)^n = a^{m \cdot n} \)
Theorems
Laws of Exponents
Suitable Grade Level
Grades 8-10
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