Laws of Laws of ExponentsExponents

VocabularyVocabulary

Factor:Factor: an integer that divides into another an integer that divides into another integer with no remainder.integer with no remainder.

24

1, 2, 3, 4, 6, 8, 12, 24

Exponent:Exponent: tells how many times to multiply a tells how many times to multiply a number by itselfnumber by itself

Base:Base: the number that is multiplied the number that is multiplied by itselfby itself

Power:Power: an expression using a base an expression using a base and an exponentand an exponent

45 = 4 • 4 • 4 • 4 • 4

26

63

Expressions with ExponentsExpressions with Exponents

(-6)(-6)44

-6-644

(-6)• (-6)• (-6)• (-6)(-6)• (-6)• (-6)• (-6)

-(6)• (6)• (6)• (6)-(6)• (6)• (6)• (6)

*They are not the same.*They are not the same.

36 • 3636 • 36

-(36 • 36)-(36 • 36)

1,2961,296

-1,296-1,296

Exponents and MultiplicationExponents and Multiplication

To Multiply powers with the SAME To Multiply powers with the SAME base:base:**Add the exponents and keep the **Add the exponents and keep the

base**base**Examples: 1) 3Examples: 1) 322 ∙ 3∙ 36 6 = 3= 388

2) a2) amm ∙ a ∙ ann = a = am + m +

nn

Exponents and DivisionExponents and Division

To Divide powers with the SAME base:To Divide powers with the SAME base:

**Subtract the exponents and keep the **Subtract the exponents and keep the base**base**

Examples: 1) Examples: 1) 8 8 55 = 8 = 8 22

8 8 33

2) 2) a a m m = a = a m - nm - n

a a nn

Zero as an ExponentZero as an Exponent

For any non-zero number a, a For any non-zero number a, a 00 = 1 = 1

Examples: 1) 9 Examples: 1) 9 00 = 1 = 1

2) 15 2) 15 00 = 1 = 1

3) 1 3) 1 00 = = 11

Negative ExponentsNegative Exponents

For any non-zero number For any non-zero number aa and and integer integer nn,,

a a –n–n = = 1 1

aann

Example: 8Example: 8 -5 = -5 = 1 1

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