Algebra 2
150
Properties of Powers
1. Product of Powers
2. Power of a Product
3. Power of a Power
4.
Negative Exponent
5.
Quotient of Powers
6.
Power of a Quotient
7.
Zero Exponent
(am)(an) = am+n
(ab)p = apbp
(am)n = amn
1
a-n =
an
am
= a m−n , a ≈ 0
n
a
n
an
⎛ a ⎞
⎜ ⎟ = n , b ≠ 0
⎝ b ⎠
b
a0 = 1, a ≈ 0
Simplifying Products and Quotients
1.
3 • 12 = 3 • 12 = 36 = 6
3
2.
5 • 3 25 = 3 5 • 25 = 3 125 = 5
4
3.
27 • 4 3 = 4 27 • 3 = 4 81 = 3
98
4.
5.
6.
7.
8.
2
4
4
98
=
2
=
=
4
1024
3
625
4
7 =7
4
=
1024
4
1
1
=
256 4
625 3
= 125 = 5
5
5
3
135 = 3 27 • 5 = 33 5
5
5
5
5
7 54
7
28
28
=
=
=
•
5
5
5
2
8 54
8
32
3
=
3
a b + c d & a b − c d are conjugates of each other.
When a denominator is a sum or a difference involving square roots, we multiply both the numerator and the the
denominator by the conjugate of the denominator.
5− 3
1
1
5− 3
5− 3
1.
=
=
=
•
2
22
5 + 3 5 + 3 5 − 3 52 − 3
( )
2.
1
7 −2
=
1
7 −2
•
7 +2
7 +2
=
7 +2
2
( 7)
− 22
=
7 +2
3
Radical expressions with the same index and radicand are like radicals. To add or subtract like radicals, we use
the distributive property as we normally did with like terms.
4
1.
10 + 74 10 = (1 + 7) 4 10 = 84 10
2.
3.
4.
5.
( ) ( )
( ) ( )
5 71/ 3 + 6 71/ 3 = (5 + 6) 71/ 3 = 11 71/ 3
26 17 + 96 17 = (2 + 9)6 17 = 116 17
48 − 4 3 = 4 16 • 3 − 4 3 = 24 3 − 4 3 = ( 2 − 1) 4 3 = 4 3
3
54 − 3 2 = 3 27 • 2 − 3 2 = 33 2 − 3 2 = (3 − 1)3 2 = 23 2
4
Simplify the Following
4
1.
27 • 4 3 = 4 81 = 3
2. 2(81/5) + 10(81/5) = 12(81/5)
3
3.
4.
5.
6.
250
3`
125 = 5
2
3
104 = 3 8 • 13 = 23 13
5
3 5 3 5 8 5 24
24
5
=
=
=
•
2
4
8
32
4
2/3
2/3
2/3
4(9 ) + 8(9 ) = 12(9 ) = 12 3 81 = 12 3 27 • 3 = 12 • 33 3 = 363 3
3
=
Algebra 2 Assignment 150 Tuesday January 5 2016 Hour
Simplify the following.
1.
(92)1/3 =
2.
(122)1/4 =
3.
4.
5.
6.
7.
6
6
7
⎛ 9 3 ⎞
⎜ ⎟
⎜ 6 3 ⎟
⎝ ⎠
−1 / 3
=
49 3 / 8 • 49 7 / 8
75 / 4
11
9− 6
8+ 7
=
3
16 • 3 32 =
3
6 • 3 72
3
=
=
2
10.
11.
=
71/ 3
8.
9.
=
1/ 4
2
3
3 • 3 18
6
2 •6 2
=
=
12.
5 12 − 19 3 =
13.
5
14.
5(241/3) – 4(31/3) =
224 + 35 7 =
Name