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Multiplying Same Base Powers

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Multiplying Same Base Powers

Mathematical powers and exponents illustration

📚 Part 1: Understanding the Rule

I can multiply powers with the same base by adding exponents.

Rule: When multiplying powers with the same base, add the exponents: a^m × a^n = a^(m+n)

1. Complete the pattern: 2³ × 2² = 2 × 2 × 2 × 2 × 2 = 2____

2⁴

2⁵

2⁶

4⁵

2. When multiplying powers with the same base, what do we do with the exponents?

Add them

Subtract them

Multiply them

Divide them

3. Which shows the correct application of the rule?

3² × 3³ = 3⁵

3² × 3³ = 9⁵

3² × 3³ = 3⁶

3² × 3³ = 6⁵

✏️ Part 2: Apply the Rule

4. Solve these multiplication problems by adding exponents:

a) 2² × 2³ = 2____ = ____

b) 4³ × 4¹ = 4____ = ____

c) 5² × 5² = 5____ = ____

d) 10² × 10³ = 10____ = ____

5. Show your work for this problem:

6² × 6⁴ = ?

6. Fill in the missing exponent:

7³ × 7____ = 7⁸

7. Circle all expressions that equal 8⁶:

8² × 8⁴

8³ × 8³

8¹ × 8⁵

8⁰ × 8⁶

🎯 Part 3: Challenge & Extension

8. Extension: Can you solve this three-factor problem?

3² × 3¹ × 3³ = 3____

9. Explain in your own words why we add exponents when multiplying same base powers:
10. Real-world connection: A bacteria population doubles every hour. If you start with 2³ bacteria and after 2 hours you have 2³ × 2² bacteria, how many bacteria do you have? Show your work.

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