Math Problem Statement
Simplify the expression \(\frac{2^5 \cdot 2^3}{2^2 \cdot 2^4}\).
Solution
The expression provided in the image is:
To simplify this, let's follow the rules of exponents:
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Combine the exponents in the numerator and the denominator:
- In the numerator: .
- In the denominator: .
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Now, simplify the fraction:
-
Calculate :
So, the simplified result is .
Would you like further details or have any questions?
Here are 5 related questions to explore:
- How do you multiply powers with the same base?
- What is the rule for dividing powers with the same base?
- How would the result change if the exponents in the numerator and denominator were different?
- What happens if the base numbers are different in such expressions?
- How do negative exponents affect such calculations?
Tip: When multiplying powers with the same base, you add their exponents; when dividing, you subtract the exponents.
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Math Problem Analysis
Mathematical Concepts
Exponents
Multiplication of Powers
Division of Powers
Formulas
Multiplying powers: a^m \cdot a^n = a^{m+n}
Dividing powers: \frac{a^m}{a^n} = a^{m-n}
Theorems
Laws of Exponents
Suitable Grade Level
Grades 6-8