Math Problem Statement
Solution
The expression given in the image is:
We will simplify this expression step by step:
Step 1: Rewrite the terms with negative exponents
Recall that . So, the terms can be rewritten as:
The entire expression now becomes:
Step 2: Simplify powers
Now calculate the powers:
- , so
- , because raising a negative number to an even power results in a positive number.
The expression now simplifies to:
Final Answer:
The expression simplifies to , so the correct answer is:
Would you like further details or have any questions?
Here are 5 related questions to expand your understanding:
- What is the rule for handling negative exponents?
- How do we simplify expressions with exponents and fractions?
- What happens when we raise a negative base to an even power?
- How do we combine powers with the same base in multiplication and division?
- What is the difference between positive and negative exponents?
Tip: When simplifying fractions with exponents, always look for common bases to make calculations easier!
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Math Problem Analysis
Mathematical Concepts
Exponent Rules
Negative Exponents
Multiplication and Division of Powers
Formulas
a^(-n) = 1 / a^n
(-a)^n = a^n when n is even
Theorems
Properties of Exponents
Simplifying Rational Expressions
Suitable Grade Level
Grades 8-10
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