The Power of Powers: Exponent Rules
Discover why multiplying powers with the same base means adding their exponents.
Equation
y = x^2 * x^3
Graph
Table
| x | y |
|---|---|
| 1 | 1 |
| 2 | 32 |
| 3 | 243 |
| 4 | 1024 |
| 5 | 3125 |
What this lesson covers
What you do
You shape the function y = x^a * x^b and watch the graph answer.
Challenges to clear
- Make the total exponent 7: choose a and b so that x^a · x^b = x^7.
- Check it on the curve: 2^7 = 128 — the graph must pass through (2, 128).
- Fix the first exponent: slide a to 4.
- Now slide b until x = 2 reads 512. Multiplying powers ADDS the exponents, and 512 is 2 to the ninth.
Check yourself
If you multiply 2^3 by 2^4, what is the correct simplified form?
- 2^7 (because you add the exponents) — correct
- 2^12 (because you multiply the exponents)
- 4^7 (because you add the bases and exponents)
- 4^12 (because you multiply the bases and exponents)
Think about it
- What happens to the result if you increase the first exponent 'a'?
- What happens to the result if you increase the second exponent 'b'?