A Guide to the GRE/Exponents

Exponents The GRE frequently tests exponents, which are numbers indicating how many times a value has been multiplied into a given system. Rule When multiplying exponents, add the exponent numbers; when raising exponents to a power, multiply the exponent numbers. An exponent is a statement of how many times a number has been multiplied into a given system. 25 is equal to 52 or 5(5). Multiplying 52 by 52 equals 5(5)(5)(5) or 54. Raising an exponent to a power multiplies the exponent numbers, while multiplying exponents merely adds their numbers. a3(a4) = a7 (b5)6 = b30 A negative exponent equals one divided by the number raised to that exponent; a fractional exponent indicates a radical of the corresponding degree. Exponent of "0" is equal to 1 A number with an exponent of “0” equals 1. x0 = 1 Practice 1. What does y2(y5) equal? 2. If (m4)4 = mx what does x equal? 3. If is equal to q−2 then what does q equal? Answers to Practice Questions 1. y7 When multiplying, add the exponent numbers. 2. 16 When raising exponents to a power, multiply the exponent numbers. 3. Negative exponents indicate 1 divided by the number raised to this exponent. q−2 is so since q−2 = , then q2 must equal 2 and q must equal .