When you understand and use rules for working with exponents, they make evaluating expressions with exponents easier and faster. The Rule of 1, Product rule, Power rule, Quotient rule and the negative exponent rule provide shorter ways to simplify expressions with exponents or raised to a power First any number raised to the power of one equals itself, x 1 =x ,therefore, 10 1= 10 . At the same time, one raised to any power (number) equals one, it means that: 1 3 =1*1*1=1. The product rule simply says that when multiplying two powers that have the same base you add the exponents, a 4 *a 3 = a (4+3) =a 7, for example, 22*2 2 =2 (2+2) =2 4. To raise a power to a power, you need to use the power rule, you need to just multiply the exponents , (2 x ) y equals 2 xy to mean that: (2 2 ) 3 =2 (2*3) =2 6 .
When dividing two powers with the same base, you need to use the quotient rule by subtracting the exponent 2 q /2 r equals 2 (q-r) , to evaluate 3 4 /3 2 = 3 (4-2) = (3*3
*3*3)/ (3*3) =
3 2 . To evaluate a number raised to a negative exponent, get the reciprocal of the number raised to the opposite power, 3 -y equals 1/3 y to evaluate
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4 -2 = 1/4 2 = 1/ (4*4) = 1/16 as told by the negative exponent rule which applies to any nonzero number. For the zero rule, any nonzero number raised to power zero equals 1, that is y 0 equals 1, hence to evaluate 10 0 : 10 0 = 1.
