Multiply Powers: Same Base Rule
See why 2^3 * 2^4 is not 2^12. Expand, count, and discover the exponent addition rule.
Equation
y = 2^(1 + x)
Graph
Table
| x | y |
|---|---|
| 0 | 2 |
| 1 | 4 |
| 2 | 8 |
| 3 | 16 |
| 4 | 32 |
| 5 | 64 |
What this lesson covers
What you do
You shape the function y = 2^(m + x) and watch the graph answer.
Challenges to clear
- Set m = 3. The table now shows 2^3 × 2^x. At x = 4 you should see 128 — that is 2^7, NOT 2^12!
- Count the twos: at x = 1, 2^3 × 2^1 = 2^4 = 16.
- Swap the base to 3 — slide b there.
- Now slide m until x = 2 reads 81. Multiplying 3² by 3² ADDS the exponents to give 3⁴, not 3⁴ times over.
Check yourself
Why does it matter that the BASE is the SAME in the product law?
Evaluate using the law: 2^6 = 2^(2+4) = 2^2 × 2^4 = 4 × 16 = ?
- Because if bases are different (e.g., 2^3 * 3^2), you cannot combine them into a single power like 6^5. — correct
- Because the base determines the color of the graph.
- Because different bases always result in zero.
- It doesn't matter; the law works for any bases.
- 64 — correct
- 20
- 12
- 32
Think about it
- 2^m × 2^x is m + x twos all multiplied together. With m = 3, how many twos are in 2^3 × 2^4?