PreAlgebra

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Chapter 7 Powers and Square Roots

You have already seen that multiplication can be considered a souped-up form of addition. In effect, multiplication allows you to quickly add a series of identical numbers. multiplying 8 x 3 = 24 is certainly a lot more convenient and faster than adding 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 24. This same idea applies to powers and roots--they are souped-up versions of multiplication and division.

7-1 Introducing Power Notation

Definition

Power notation--the method for indicating the power of a number--has two parts:

The base indicates the number to be multiplied.
The exponent indicates the number of times the base is to be multiplied.

More Examples

3² = 3 x 3 = 9

2⁴ = 2 x 2 x 2 x 2 = 16

4⁵ = 4 x 4 x 4 x 4 x 4 = 1024

Notes

Notation

Explanation

Example

n¹ = n

Any number with an exponent of 1 is equal to that number, itself.

5¹ = 5

n⁰ = 1

Any number with an exponent of 0 is equal to 1.

3⁰ = 1

1^k = 1

1 to any power is equal to 1.

1⁴ = 1

0^k = 0

0 to any power is equal to 0.

0⁵ = 0

	n^-k =	1
		n^k

Any number with a negative exponent is equal to 1 divided by that number with a positive exponent.

2^-3 =	1	= 0.125
	2³

Author: David L. Heiserman
Publisher: SweetHaven Publishing Services