Exponent Rules & Scientific NotationGeoff Clement, July 2013

“The Big Three”

am an _____

am

an _____

am n_____

We assume a ≠ 0.

Examples

_____5

_____8

8

_____ 2222

43

2

10

234

Examples

x5 x4 x3 x2 x _____

y6

y2 _____

b2 3_____

Related Rules

a0 _____

a–n _____ 1

a–n _____

a–n

b–m _____We assume a ≠ 0 and b ≠ 0.

The Home Stretch

ab n _____

a

b

n

_____

a

b

–n

_____

We assume a ≠ 0 and b ≠ 0.

Examples

5 + 2 0 _____

m–6

y–2 _____

3–1 2–1 _____

Examples

2x2y3z 4 _____

x

2

3

_____

x

2

–3

_____

A mixture of many of the

rules . . .

________106.1105 _____333

_____33

3–3 _____

5

5

54777

9981000

9981000

2–

2

Scientific Notation

We assume 1 ≤ a < 10 and b is an integer.

b10a

1223

05

109 106.02

101.5 101.5

notation. decimal standard Convert to

Scientific Notation

We assume 1 ≤ a < 10 and b is an integer.

b10a

0,000700,000,00 50,0004

08.0000000000 .000230

notation. scientific Convert to

Fascinating Examples

The body of a 150-lb person contains 2.3 x 10–4 lb of copper. What percent of the person’s body weight is composed of copper?

Fascinating Examples

In a recent tax year, the IRS averaged collecting $7,000 per person in the U.S. If the population of taxpayers in that year was 140,000,000, find the total revenue they collected.

Fascinating Examples

1 “light year” is defined as the distance light travels in one Earth year. The speed of light is roughly .

Approximate the number of miles in a light year.

mph106.7 8