laws of exponents. vocabulary factor:an integer that divides into another integer with no remainder....
TRANSCRIPT
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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