A2notes - Supplementary Course Module A Simplifying Numeric...

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Supplementary Course Module A: Simplifying Numeric Expressions Assignment 2 ° Powers & Roots Powers: ° Exponents, or powers, represent the operation of repeated multiplication. examples: 6 2 = 6 ± 6 = 36 (squaring), ( ² 4) 3 = ( ² 4) ± ( ² 4) ± ( ² 4) = ² 64 (cubing) ° In the °rst example above, the ± 6 ² is termed the base while the ± 3 ² is termed the exponent or power. The exponent is only applied to the base itself. examples: ( ² 3) 2 = ( ² 3) ± ( ² 3) = 9 , ² 3 2 = ² (3 ± 3) = ² 9 ° Arithmetic operations involving exponents are summarized below: Rule Example 1. a m ³ a n = a m + n 5 10 ³ 5 4 = 5 10+4 = 5 14 2. a m a n = a m ° n 5 10 5 4 = 5 10 ° 4 = 5 6 3. ( a m ) n = a m ± n ° 5 10 ± 4 = 5 10 ± 4 = 5 40 4. a 0 = 1 5 0 = 1 5. ( a ³ b ) m = a m ³ b m ² a b ³ m = a m b m (5 ³ 8) 4 = 5 4 ³ 8 4 6. ² a b ³ ° n = ´ b a µ n ´ 5 8 µ ° 3 = ´ 8 5 µ 3 = 8 3 5 3 ° rule #5 shows that exponentiation distributes over multiplication and division exponentiation does not distribute over addition and subtraction ( a + b ) m 6 = a m + b m ( a ² b ) m 6 = a m ² b m °
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