Power of a Quotient
Simplify (2x/3)^3 using exponent laws step-by-step.
Equation
y = (x/2)^1
Graph
Table
| x | y |
|---|---|
| 0 | 0 |
| 1 | 0.5 |
| 2 | 1 |
| 3 | 1.5 |
| 4 | 2 |
| 5 | 2.5 |
| 6 | 3 |
What this lesson covers
What you do
You shape the function y = (x/b)^n and watch the graph answer.
Challenges to clear
- Set b = 3 and n = 3. Then (x/3)³ at x = 6 is (6/3)³ = 2³ = 8.
- That is the quotient rule: x³/3³ = 216/27 = 8. And at x = 3: (3/3)³ = 1.
- Halve the input first: slide the divisor b to 2.
- Now slide n until x = 6 reads 81. (6/2)ⁿ = 3ⁿ, and 81 is 3 to the fourth — the power reaches top AND bottom.
Check yourself
Why does it matter that the BASE is the SAME in the power of a power law?
Evaluate using the law: (2^2)^3 = 2^(2*3) = 2^6 = ?
- Because exponents only multiply when the base is identical. — correct
- Because you can add the bases instead.
- It doesn't matter, the law works for any bases.
- Because the result is always zero.
- 32
- 64 — correct
- 12
- 8
Think about it
- (6/3)³ means (6/3) × (6/3) × (6/3). What is it?