Dividing Powers: The Subtraction Trick
See why dividing same bases means subtracting the exponents.
Equation
y = x^3 / x^2
Graph
Table
| x | y |
|---|---|
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
What this lesson covers
What you do
You shape the function y = x^m / x^n and watch the graph answer.
Challenges to clear
- Set m = 5 and n = 2. At x = 2 the table must show 8 — because 2^5 / 2^2 = 2^(5−2) = 2^3.
- Same subtraction at x = 3: you should see 27, which is 3^3.
- Two factors cancel from the bottom — slide n to 2.
- Now slide m until x = 2 reads 16. Dividing SUBTRACTS the exponents: m − 2 = 4, so m is 6.
Check yourself
If m=5 and n=2, the result is x^3. Which calculation proves this is correct?
- 2^5 / 2^2 = 32 / 4 = 8, which equals 2^3 — correct
- 2^5 / 2^2 = 32 / 4 = 8, which equals 2^4
- 2^5 / 2^2 = 32 / 4 = 8, which equals 2^2
- 2^5 / 2^2 = 32 / 4 = 8, which equals 2^5
Think about it
- x^5 / x^2 cancels two x's from top and bottom. How many x's remain?