Math Problem Statement

Simplify the expressions 2^3 ⋅ 2^5 and 3^2 ⋅ 3^3.

Solution

In the image, two math problems are visible. I'll solve them below:

  1. Problem 1.35: 23252^3 \cdot 2^5 Using the property of exponents, aman=am+na^m \cdot a^n = a^{m+n}, we get: 2325=23+5=28=2562^3 \cdot 2^5 = 2^{3+5} = 2^8 = 256 Solution: 256256

  2. Problem 1.36: 32333^2 \cdot 3^3 Again, applying the property of exponents: 3233=32+3=35=2433^2 \cdot 3^3 = 3^{2+3} = 3^5 = 243 Solution: 243243

Would you like further explanations or details? Here are some related questions:

  1. How do you simplify expressions involving exponents?
  2. What are the rules for multiplying powers with the same base?
  3. How do negative exponents work?
  4. Can you explain how powers of a number grow exponentially?
  5. How would you approach expressions with different bases?

Tip: Always remember to apply exponent rules, like aman=am+na^m \cdot a^n = a^{m+n}, to simplify expressions quickly.

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Math Problem Analysis

Mathematical Concepts

Exponents
Multiplication of Powers

Formulas

a^m ⋅ a^n = a^(m+n)

Theorems

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Suitable Grade Level

Grades 6-8