exponents and radicals class 8
. WHAT IS AN EXPONENT? An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 2 3 ) means: 2 x 2 x 2 = 8 . 2 3 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself. For example, a 1 = a 5 1 = 5 . There are some special cases: 1. a 0 = 1 When an exponent is zero, as in 6 0 , the expression is always equal to 1. a 0 = 1 6 0 = 1 14,356 0 = 1 2. a -m = 1 / a m When an exponent is a negative number, the result is always a fraction. Fractions consist of a numerator over a denominator. In this instance, the numerator is always 1. To find the denominator, pretend that the negative exponent is positive, and raise the number to that power, like this: a -m = 1 / a m 6 -3 = 1 / 6 3 You can have a variable to a given power, such as a 3 , which would mean a x a x a. You can also have a number to a variable power, such as 2 m , which would mean 2 multiplied by itself m times. We will deal