The Power of Negative Exponents
Slide the exponent to discover what happens when powers go below zero.
Equation
y = 2^(x + 1)
Graph
Table
| x | y |
|---|---|
| -3 | 0.25 |
| -2 | 0.5 |
| -1 | 1 |
| 0 | 2 |
| 1 | 4 |
| 2 | 8 |
| 3 | 16 |
What this lesson covers
What you do
You shape the function y = 2^(x + n) and watch the graph answer.
Challenges to clear
- Slide n to −1: the whole curve halves. At x = 0, y = 2⁻¹ = 0.5.
- Negative powers are small but NEVER negative: at x = −2 the total power is 2⁻³ = 0.125.
- Swap the base: slide b to 3.
- Now shift the curve so x = 0 reads one third. A negative power flips the base into a fraction — but never makes it negative.
Check yourself
Why does 2^-1 equal 1/2 instead of -2? Think about the pattern of division.
- Negative exponents mean you subtract the base from zero.
- Each step down divides by the base, so 2^0 / 2 = 1/2. — correct
- The negative sign flips the base to -2, so 2^-1 is -2.
- Negative exponents are just errors in calculation.
Think about it
- If n is positive, y is a whole number at x = 0. What happens as n goes negative?