Question

What is a true statement about negative exponents?

Answer 1

Answer:

Raising something to a negative exponent is just taking the reciprocal of the amount.

Step-by-step explanation:

Let's assume that you wanted to know what $x^{-2}$ is.

To find it, you would take the reciprocal of the x amount. So $x^{-2}$ becomes $\frac{1}{x^{2}}$.

This works because of the nature of exponents. Exponents represent the number of times you are multiplying a value by itself. So $a^{3}$ would be equal to a · a · a. To increase the exponent, you increase the number of times the value is multiplied by itself: To increase $a^{3}$ to $a^{5}$, you would have to multiply a with $a^{3}$ two more times (a · a · a · a · a). To decrease the exponent, you must divide the value by itself. So to decrease $a^{5}$ to $a^{2}$, you would have to divide $a^{5}$ by a 3 times.

If the exponent is 0, the value is equal to 1. But you can still decrease the exponent into negative numbers. You just divide 1 by a the desired amount of times: $\frac{1}{a^{3}}$ means that you are dividing 1 by a 3 times.

Hope this helps.