Technical Mathematics, Sixth Edition

1.5. Powers and Roots

Now that we know how to do the four basic arithmetic operations on signed and approximate numbers, let us learn how to find powers and roots.

1.5.1. Powers

▪ Exploration:

Try this. Use your calculator to multiply 2 × 2 × 2. Then use it to evaluate 2³. You can do this using the key on your calculater, as shown on the screen. Then evaluate 2 × 2 × 2 × 2, as well as 2⁴.

Can you summarize what you have found?

In the expression

2⁴

the number 2 is called the base, and the number 4 is called the exponent. The expression is read "two to the fourth power." Its value is

2⁴ 2 · 2 · 2 · 2 = 16

To square a number means to raise it to the power 2. To cube a number means to raise it to the power 3.

TI-83/84 screens for the Exploration.

TEACHING TIP: Emphasize that the base is multiplied, not added. Thus 23 = 2(2)(2) = 8, not 2 + 2 + 2 = 6.

Stated as a formula,

NOTE

Example 47: 34 = 3 · 3 · 3 · 3 = 81 53 = 5 · 5 · 5 = 125 45 = 4 · 4 · 4 · 4 · 4 = 1024

When raising an approximate number to a power, round your answer to the number of significant digits in the base, not the exponent.

TI-83/84 screen for Example 48.

Example 48: Use your calculator to verify the following: ...