Thinking negative index gives negative answer H
"The Negative Confusion"
The Mistake in Action
Evaluate $4^{-2}$
Wrong: $4^{-2} = -16$
Why It Happens
Students confuse a negative index with a negative answer. They may think $4^{-2}$ means "negative $4^2$".
The Fix
A negative index means "one over" (reciprocal), NOT a negative answer.
$$a^{-n} = \frac{1}{a^n}$$
$$4^{-2} = \frac{1}{4^2} = \frac{1}{16}$$
Note: $4^{-2}$ is a positive number (since we're dividing 1 by a positive number).
$-4^2$ (negative $4^2$) = $-16$ $4^{-2}$ (4 to the power of $-2$) = $\frac{1}{16}$
Spot the Mistake
Can you identify where this student went wrong?
Evaluate $4^{-2}$
$= -16$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: