What is a true statement about negative exponents?

Accepted Solution

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 [tex]x^{-2}[/tex] is. To find it, you would take the reciprocal of the x amount. So [tex]x^{-2}[/tex] becomes [tex]\frac{1}{x^{2}}[/tex]. This works because of the nature of exponents. Exponents represent the number of times you are multiplying a value by itself. So [tex]a^{3}[/tex] 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 [tex]a^{3}[/tex] to [tex]a^{5}[/tex], you would have to multiply a with [tex]a^{3}[/tex] two more times (a · a · a · a · a). To decrease the exponent, you must divide the value by itself. So to decrease [tex]a^{5}[/tex] to [tex]a^{2}[/tex], you would have to divide [tex]a^{5}[/tex] 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: [tex]\frac{1}{a^{3}}[/tex] means that you are dividing 1 by a 3 times. Hope this helps.