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Aviation Maintenance Technician Handbook–General

FAA-H-8083-30B Version 2023
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Chapter 3

Mathematics in Aviation Maintenance

Power of Zero

Any non-zero number raised to the zero power always equals 1.

Formula: Example: ; 70 = 1 1810 = 1 (–24)0 = 1

Negative Powers

A number with a negative power equals its reciprocal with the same power made positive.

Example: The number 2-3 is read as “2 to the negative 3rd power,” and is calculated by:

Formula: 2-3 = 1 = 1 = 1 ; 23 2 × 2 × 2 8

When using a calculator to raise a negative number to a power, always place parentheses around the negative number (before raising it to a power) so that the entire number gets raised to the power.

Law of Exponents

When multiplying numbers with powers, the powers can be added as long as the bases are the same.

Formula: Example: ; 32 × 34 = (3 × 3) × (3 × 3 × 3 × 3) = 3 × 3 × 3 × 3 × 3 × 3 = 36 ; or 32 × 34 = 3(2+4) = 36
Figure 3-8. A scale of signed numbers.
Figure 3-8. A scale of signed numbers.

When dividing numbers with powers, the powers can be subtracted as long as the bases are the same.

Example:

Formula: 104 ÷ 102 = 10 × 10 × 10 × 10 = 10 × 10 × 10 × 10 =10 × 10 =102 ; 10 × 10 10 × 10 ; or 104 ÷ 102 = 10(4 – 2) = 102

Powers of Ten

Because we use the decimal system of numbers, powers of ten are frequently seen in everyday applications. For example, scientific notation uses powers of ten. Also, many aircraft drawings are scaled to powers of ten. Figure 3-9 gives more information on the powers of ten and their values.

Roots

A root is a number that when multiplied by itself a specified number of times produces a given number.

The two most common roots are the square root and the cube root. For more examples of roots, see Figure 3-10.