Math Problem Statement
Solution
Let's solve the expression shown in the uploaded image step by step.
The given expression is:
Step 1: Simplify powers
We will simplify the terms involving exponents first.
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Simplify :
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Express 18 in terms of its prime factors:
Now the expression becomes:
Step 2: Express 24 in terms of prime factors
Now the expression becomes:
Step 3: Simplify the terms involving the same bases
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Simplify the powers of 2:
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Simplify the powers of 3:
Now the expression becomes:
Step 4: Evaluate the result
Thus:
Final Answer
Would you like any further steps or clarifications? 😊
Here are 5 follow-up questions for deeper exploration:
- How do the rules of negative exponents work in general?
- How do you factor numbers into their prime factors efficiently?
- What is the significance of the order of operations when simplifying powers?
- Can you generalize how to simplify expressions with multiple exponents?
- How would the result change if one of the exponents was zero?
Tip: When dealing with powers, always group similar bases to simplify calculations easily.
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Math Problem Analysis
Mathematical Concepts
Exponents
Simplification
Prime Factorization
Formulas
a^m / a^n = a^(m-n)
(a^m)^n = a^(m×n)
Prime factorization of numbers
Theorems
Exponent Rules
Prime Factorization
Suitable Grade Level
Grades 9-11
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