Math 017 Materials With Exercises

Lesson 4__________________________________________________________________________________Topics: Operations on power expressions with non-negative integer exponents.__________________________________________________________________________________Exponential notationExponential notation is used to write repeated factors in a compact way. Exponents are another way ofwriting multiplication. For example,2 52 2 2 2 2, 3 2 3 3.25times timesWe will extend this idea to algebraic expressions.Exponential ExpressionThe expression of the form a n is called an exponentialexpression. It is defined as followsa0 1,1a a ,2a a a ,…na a a ... a , for n = 1, 2, 3, … .ntimes(a is repeated as a factor n times).a is called the base, n is called an exponent or power.Notice that, according to the definition any expression raised to the zero-th power is equal to one. Also,a variable that appears to have no exponent is raised to the first power.a 1 = an2Recall that a is read as “ a to the n-th power”. In the case of a , often, instead of “ a to the second3power” we read it as “ a squared”; a is often read as “ a cubed”.You should also remember that:The exponent pertains only to “the closest” number or variable. To apply the exponent to theentire expression we must place parentheses around the expression. The exponent is then placedoutside the parentheses.For example,3in 2b , only b is raised to the third power.3in ( 2b ) , 2bis raised to the third power.orininn x , only x is raised to the n-th power (n pertains only to x not to x)n( x) , x is raised to the n-th power38