Math Problem Statement
Solution
Let’s simplify the given expression step by step.
The expression is:
Step 1: Combine like terms (grouping same bases)
-
For :
- .
-
For : (foul); It seems like I started off-track when combining terms due to notation confusion. Let’s simplify correctly:
The expression given is:
Let me interpret and rewrite it step by step.
Step 1: Simplify constants
Combine the numerical coefficients:
So, the updated expression is:
Step 2: Combine powers for like bases
-
For : Add the exponents and :
-
For : Add the exponents and :
-
remains as .
Step 3: Use only positive exponents
- becomes .
So, the fully simplified expression is:
Let me know if you have questions or would like further clarification!
Related Questions:
- How can I verify if my simplified expression is correct?
- What are the rules for adding and subtracting exponents when simplifying?
- How do negative exponents translate into fractions?
- Are there any shortcuts for simplifying expressions with multiple variables?
- Can we visualize how exponents combine using expanded forms?
Tip: Always combine like terms by ensuring all variables with the same base are grouped together before simplifying.
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Math Problem Analysis
Mathematical Concepts
Exponent Rules
Algebraic Simplification
Formulas
Product of powers: \(a^m \cdot a^n = a^{m+n}\)
Negative exponents: \(a^{-m} = \frac{1}{a^m}\)
Theorems
Laws of Exponents
Suitable Grade Level
Grades 8-10