algebra 2: section 6.1 properties of exponents. product of powers –(when multiplying like bases,...
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Properties of ExponentsProperties of Exponents
Product of PowersProduct of Powers– (when multiplying (when multiplying
like bases, add like bases, add exponents)exponents)
Power of a PowerPower of a Power– (when taking an (when taking an
exponent to a exponent to a power, multiply the power, multiply the exponents)exponents)
m n m na a a
( )m n mna a
Properties of ExponentsProperties of Exponents
Power of a ProductPower of a Product– (distribute)(distribute)
Negative ExponentNegative Exponent– (flip to opposite (flip to opposite
side)side)
( )m m mab a b
1mm
aa
Properties of ExponentsProperties of Exponents
Zero ExponentZero Exponent– ((anythinganything taken to taken to
the zero power is 1)the zero power is 1)
Quotient of PowersQuotient of Powers– (when dividing like (when dividing like
bases, subtract bases, subtract exponents)exponents)
0 1a
mm n
n
aa
a
Properties of ExponentsProperties of Exponents
Power of a Power of a QuotientQuotient– (distribute)(distribute)
m m
m
a a
b b
Rules for Simplifying Exponential Rules for Simplifying Exponential ExpressionsExpressions
NO negative exponentsNO negative exponents
Simplify all numbers taken to a Simplify all numbers taken to a powerpower
Variables go in Variables go in alphabeticalphabetic order order
Only one occurrence of each Only one occurrence of each variable in a single termvariable in a single term
Examples:Examples:32
3
a4.
b
6
9
a
b 6 9a b
2 5 2 125. ( )y y y 10 10y y
1
2
1 36.
( )
rs
rs
2
3 3
rs
r s
5
2
s
r
0y
2 3
3
rs s
r
MOREMORE Examples: Examples:
2 4 38. 2 4ab a b c
2 39. 6x y xyz
11
510.
x
x
15
2211.
y
y
5 58a b c
3 46x y z
6x 7
1
y
MORE Examples:MORE Examples:
3412. x
43 213. 2a b
23
6 3
314.
6
x y
x y
34
15.n
12x3
64
n
12 816a b
6 8
4
x y