Math Problem Statement
Solution
Let's analyze the mathematical expression provided in the image and simplify it.
The given expression is:
Step-by-Step Simplification:
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Simplify the exponents inside the parentheses: The expression inside the parentheses is .
- The negative exponent of means .
- The negative exponent of means .
This transforms the expression to:
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Apply the exponent -2 to the whole expression: Now, we need to apply the exponent of to the entire fraction .
Using the power rule , we apply the exponent to both the numerator and denominator:
Simplifying both the numerator and denominator:
So the expression becomes:
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Convert to positive exponents: Now, to express everything with positive exponents, we get:
Thus, the simplified expression with all positive exponents is:
Would you like further details or have any questions?
Here are 5 related questions to explore:
- How do you apply negative exponents to a fraction?
- What is the general rule for simplifying an expression with multiple terms raised to a negative exponent?
- How does changing the exponent sign affect the position of variables in the numerator or denominator?
- How do you simplify expressions with both positive and negative exponents?
- How does the power of a product rule work when applying exponents?
Tip: When simplifying expressions with exponents, always manage the signs carefully and apply exponent rules step by step to avoid mistakes.
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Math Problem Analysis
Mathematical Concepts
Exponents
Negative Exponents
Simplifying Fractions with Exponents
Formulas
Power of a quotient rule: \(\left( \frac{x}{y} \right)^n = \frac{x^n}{y^n}\)
Negative exponent rule: \(x^{-n} = \frac{1}{x^n}\)
Theorems
Exponentiation rules
Power of a fraction
Suitable Grade Level
Grades 10-12