Page 60 - Mathematics of Business and Finance

40 Chapter 1 | Review of Basic Arithmetic

–n
n
Therefore, a and a are reciprocals.
For example,

–1
■ 8 = 1 = 1
8 1 8
A positive number with a
negative exponent will not ■ 8 = 1 = 1
–2
result in a negative answer. 8 2 8 × 8
1 1
–3
■ 8 = =
8 3 8 × 8 × 8

Exhibit 1.4: Standard and Exponential Form of Numbers

Fractions with Exponents

When a fraction has a positive exponent, the number in the exponent indicates the number of times the
numerator is multiplied by itself and the number of times the denominator is multiplied by itself.
For example,
2 3 2 2 2 2 × 2 × 2 2 4 2 × 2 × 2 × 2
■ c m = c mc mc m = ■ =
5 5 5 5 5 × 5 × 5 3 5 3 × 3 × 3 × 3 × 3

When a fraction has a negative exponent, change the fraction to its reciprocal and drop the negative
sign in the exponent. After this change, the number in the exponent indicates the number of times the
numerator is multiplied by itself and the denominator is multiplied by itself.
For example,

3
–3
5
2
5
5
5
a –n b n ■ c m = c m = c mc mc m = 5 × 5 × 5
c m = c m 5 2 2 2 2 2 × 2 × 2
b a
2 5
Note: The reciprocal of is .
5 2
Calculator Method to Solve Problems
y
x
The exponent key on different calculators are identified by symbols such as y , x , ^, etc. The
sequence of operations to calculate the exponents also depends on the calculator. In this section,
you will learn to use the Texas Instruments BA II Plus calculator to solve exponents and order of
operations problems.

Example 1.4(c) Calculating Exponents using Texas Instruments BA II Plus Calculator
Calculate:

(i) 16 4 (ii) 5 –4 (iii) (1.04) – 1 (iv) 1 – (1.005) –4
4