Instructional Material on Exponents and Roots 1-26 Exponents described An exponent tells how many times a number is to be used as a factor. For example, in the expression 43, the exponent 3 means that we are to multiply 4 3 4 3 4. The expression 54 means 5 3 5 3 5 3 5. If the exponent is zero, the value of the expression is always 1. Thus, 30 5 100 5 1. If the exponent is 1, the value of the expression is the number whose exponent is 1. Thus, 31 5 3, and 71 5 7. Problems with exponents can be done by remembering that exponents just count factors. For example: Evaluate 34 3 33. Since 34 means use 3 as a factor four times, and 33 means use 3 as a factor three times, and since we then multiply the results, we are using 3 as a factor 3 1 4 or 7 times. Therefore 34 3 33 5 37. Similarly, 45 4 42 5 43, because we are dividing out two of the five factors of 4, leaving three factors of 4, or 43. A negative exponent indicates the reciprocal of a positive exponent. Thus, 1 522 5 2 . Note that 52 3 522 5 50 5 1. 5 SUMMARY I. If two numbers have the same base (e.g., 32, 35 or 72, 76) when we multiply, we keep the base and add the exponents: Examples: 32 3 33 5 35 221 3 222 5 223 32 3 322 5 30 5 1 25 3 223 5 22 76 3 714 5 720 II. If two numbers have the same base (e.g., 32, 35 or 72, 76) when we divide, we keep the same base and subtract the exponents:
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