Mathematics doesn't break rules. Let's observe what happens when we divide by the base repeatedly.
We start with $2^3 = 8$. Each time we step down, we Divide by 2.
Fill in the next value in the sequence.
| Action | Index Form | Expanded | Value |
|---|---|---|---|
| Start | $2^3$ | $2 \times 2 \times 2$ | 8 |
| ÷ 2 | $2^2$ | $2 \times 2$ | 4 |
| ÷ 2 | $2^1$ | $2$ | 2 |
| ÷ 2 | $2^0$ | $1$ | 1 |
| $2^{-1}$ | ??? |
So $2^{-1}$ is half of 1, which is $\frac{1}{2}$. What happens if we divide by 2 again?
Negative power doesn't mean "negative number". It means Reciprocal (1 over the number).
$x^{-n} = \frac{1}{x^n}$
Think of the negative sign in the power as a specific instruction: "FLIP ME!"
Click the card below to apply the negative sign. Watch it move downstairs.
What if the negative power is already on the bottom? $\frac{1}{x^{-3}}$
If you cross the fraction line, the sign of the power changes.