Math Problem Statement

What is the value of 2^3 × 2^2?

Solution

The expression shown in the image is:

23×222^3 \times 2^2

To solve this, we apply the property of exponents that states:

am×an=am+na^m \times a^n = a^{m+n}

Here, a=2a = 2, m=3m = 3, and n=2n = 2. So:

23×22=23+2=252^3 \times 2^2 = 2^{3+2} = 2^5

Now, 25=322^5 = 32.

Therefore, the value of the expression is:

23×22=322^3 \times 2^2 = 32

Would you like further details or have any questions?

Here are 5 related questions:

  1. What are the other properties of exponents?
  2. How do you simplify expressions with different bases?
  3. How do you deal with negative exponents?
  4. What happens when you divide powers with the same base?
  5. How do you simplify expressions with fractional exponents?

Tip: When multiplying powers with the same base, simply add their exponents for quicker simplifications.

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Math Problem Analysis

Mathematical Concepts

Exponents
Multiplication of Powers

Formulas

a^m × a^n = a^(m+n)

Theorems

Laws of Exponents

Suitable Grade Level

Grades 6-8