Exponents and Scientific Notation

Vocabulary

100

The number that gets multiplied when using an exponent. 

Base

200

Represents the number of times a base is multiplied. 

Exponent

300

A letter that represents an unknown number

Variable 

400

A number expressed using exponents. Commonly called exponent. 

Ex: 8⁵  is also known as 8 to the 5th _______

Power 

500

A number being multiplied with a variable

Ex: the 3 in 3x

Coefficient 

Exponent Rules

100

Keep the base, add the exponent

Multiplying with like bases. 

Ex: y² x y⁴

200

Keep the base, subtract the exponents

Dividing with like bases 

y⁵  ÷  y³

300

Zero exponent rule

Anything to the zero power = 1

a⁰ = 1

15⁰ = 1

400

Negative exponent rule

A negative exponent should be moved to the opposite side of the fraction

x^-2 = 1/x²

500

Power of a product

Find the power of each product = multiply the exponents

(3x)² = (3²)(x²) or 9x²

Simplifying Exponents

100

x⁷ _x x^{8 =} 

x¹⁵

200

17⁸ ÷ 17^{3 =} 

17⁵ 

300

8^-6 _x 8³ =

8^-3 or 1/8³

400

y¹⁷ ÷ y¹⁹ = 

y^-2 or 1/y²

500

(15b³)⁴ = 

15⁴b¹²  or 50625b¹²

Convert to Standard Form

100

4.2 x 10^-6

.0000042

200

1.2 x 10⁸

120000000

300

3.011 x 10⁶

3011000

400

8.1 x 10⁴

81000

500

2.1 x 10^-2

0.021

Convert to Scientific Notation

100

815,000

8.15 x 10⁵

200

0.0000702

7.02 x 10^-5

300

0.99

9.9 x 10^-1

400

23,020,000

2.302 x 10⁷

500

0.0000000032

3.2 x 10^-9