University:
California State University, Northridge
Course:
MATH 102 | Pre-Calculus I
Academic year:

2024
Views:

80

Pages:

4
Author:

Yasmin Shaffer

Math 094 - Mod. II - Chapter 1 Exponents (Module II, page 3) a) Exponential notation is another way to express repeated multiplication. For example, . In general we define exponential notation for a positive integer n as follows. (n factors ) In this expression, b occurs as a factor n times, b is called the base and n is called the exponent (or power). i.e. baseexponent or basepower So the exponent tells us how many times to use the base as a factor in an exponential expression. b) If no exponent is written, it is understood to be one. That is, b means b1. . So any non-zero number raised to the c) We define b0 = 1, for any real number 0 zero power is one. If b = 0, then 0 = undefined. Examples: 24 = Can you tell the difference between this one and -16 Yes! The parentheses make them different. Without ( ), the 2nd power is for the base 4 itself. With ( ), the base is -4. d) From the second and third example, we notice that (- #)odd power = negative result And (- #)even power = positive result Practice Problems: #1 (-1)15 = #2 04 = #3 -24 = #4 (-2)4 = #5 7470 = #6 x0 = Multiplication with Exponents (Module II, page 4) Consider the following product: 23 • 25 We recognize that: 23 = and 25 = So 23• 25 = = 23 + 5 = 28 • In general, bmbn means m factors of b times n factors of b. There are then m + n factors of b, which may be written as bm+n. When multiplying two or more expressions with the same base, simply write the base and add the exponents. Thus Let us consider other expressions that involve exponential factors. Specifically let's discuss (bm)n where m and n are natural numbers. The n means to use bm as a factor n times and the m tells us to use b as a factor m times. Therefore we have The two basic formulas for problems involving exponents are: Examples: Practice Problems: #7 #8 #9 #10 Expanded Notation And Exponents (Module II, page 5) We can write the powers of 10 using exponents. For example: 100 = 1 101 = 10 102 = 100 103 = 1000 104 = 10000 This suggests the relationship between the exponent in the power of ten and the number of zeros in the decimal number for the power; the exponent tells how many zeros occur in the number. We can use exponents in wrtiing the expanded notation of an integer. For example: Practice Problem: #11 Write 98,012 in expanded form using powers of ten. #12 Write the decimal number indicated by: Solution #1 -1 #2 0 #3 -16 #4 16 #5 1 #6 1 ( #7 58 #8 320 ) #9 #10 a6 #11 #12 1,058,203