The Power of Product Rule
See how (ab)^n splits into a^n * b^n by expanding the brackets.
Equation
y = (2*2)^x
Graph
Table
| x | y |
|---|---|
| 0 | 1 |
| 1 | 4 |
| 2 | 16 |
| 3 | 64 |
| 4 | 256 |
What this lesson covers
What you do
You shape the function y = (a*b)^x and watch the graph answer.
Challenges to clear
- Set a = 2 and b = 3. Check that (2×3)^2 = 36 in the table at x = 2.
- One more power: (2×3)^3 must be 216 — exactly 2^3 × 3^3 = 8 × 27.
- A different product inside the bracket. Set a = 2.
- Slide b until x = 2 reads 100. (2×5)² = 100, and that is exactly 2² × 5² = 4 × 25.
Check yourself
Which expression is equivalent to (4*5)^3?
Why does (ab)^n = a^n * b^n work?
- 4^3 * 5^3 — correct
- 4^3 * 5
- 4 * 5^3
- (4+5)^3
- Because you have n groups of a and n groups of b. — correct
- Because the exponent only applies to the last number.
- Because you must add the exponents first.
- Because multiplication is the same as addition.
Think about it
- (ab)^2 means (ab) × (ab). With a = 2 and b = 3, how does 36 split into a power of 2 times a power of 3?