Math Problem Statement
Solution
The problem in the image asks to simplify the expression into a form with positive exponents. Let's break it down step by step:
Expression:
Step 1: Simplify each term
-
First term:
Apply the power rule to each factor inside the parentheses: -
Second term:
Apply the power to each factor:
Step 2: Combine both terms
Now, multiply the results from both terms:
Step 3: Simplify the exponents
Use the exponent rules to simplify the powers of :
Step 4: Write the expression with positive exponents
Since the exponent of is negative, move it to the denominator:
Thus, the simplified form is:
Conclusion:
The correct option is C, which matches .
Would you like further clarification on any step?
Here are five related questions to consider:
- What are the general rules for multiplying exponents?
- How do negative exponents affect a term's position in a fraction?
- What happens when you raise a product of terms to a power?
- Can you simplify ?
- How do fractional exponents relate to roots?
Tip: Always apply the power rule individually to each factor within parentheses before simplifying.
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Math Problem Analysis
Mathematical Concepts
Exponents
Simplifying Expressions
Algebra
Formulas
Power of a Power Rule: (a^m)^n = a^{m*n}
Multiplying Powers with the Same Base: a^m * a^n = a^{m+n}
Negative Exponent Rule: a^{-n} = 1/a^n
Theorems
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Suitable Grade Level
Grades 8-10