Which expression is equivalent to x^-2? A) -x^2 {a minus power is…

Step by step

The question

Question: simplify x⁻².

There are four choices.

First we solve it, the normal way.

Then we pick.

1 Negative power

Why does a minus power mean 1 over?

Look at x² over x⁴.

Crossing out leaves 2 x's on the bottom, so it is 1/x².

With the divide rule, we take away the powers: 2 − 4 = −2.

So it is x⁻².

Both ways give the same thing.

So a minus in the power means 1 over: the x's go to the bottom.

So we get 1/x².

2 Pick the choice

Our answer is 1/x².

That is choice C.

3 Why not the others

A is −x².

Wrong: a minus power is not a minus sign.

B is −2x.

Wrong: x to the −2 is not −2 times x.

D is 1/(2x).

Wrong: x² is x × x, not 2x.

Let's look back.

First: negative power.

Then: pick the choice.

Last: why not the others.