P2 Exponents & Radicals. What does an exponent tell you?? Repeated Multiplication How many times you...
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Transcript of P2 Exponents & Radicals. What does an exponent tell you?? Repeated Multiplication How many times you...
P2Exponents & Radicals
What does an exponent tell you??
Repeated Multiplication
How many times you multiply the base by itself.
Expand the following:
5
5
5
2
)3(
y
x
odd
even
General Rule on Negatives:
Properties of Exponents
Examples
24
3
3
2
04
2
2
432
32132
6 d)
4 g) )3(6 c)
6
4 f) )2( b)
)2( e))5)(4( a)
y
x
y
axx
xyx
yxmnnm
Try Some Harder Ones4 2
1
33 2
4
3
25
15
2
4
4( )
24( )
x y
x y
x y
y
x y
x y
Scientific Notation
000,000,876,9.4
1054.6.3
00000815.0.2
10468.2.1
7
5
Radicals and their Properties
Square Root Cube Root
One of its two equal factors
One of its three equal factors
If a and b are real numbers, , then
2n1
thn
thn
a b b is the n root of a
a b b is the n root of a
n index
a radicand
Examples
45
3
16 .532.4
125
8 .349 .2 49.1
Properties of Radicals
1.
2.
3. 0
4.
5.
6. For even,
For odd,
mn m n
n n n
n
nn
m n mn
nn
n n
n n
a a
a b ab
a ab
bb
a a
a a
n a a
n a a
Let’s Look at Property #6
6. For even,
For odd,
n n
n n
n a a
n a a
Ok… think about this 49 ?
2 49x What are the solutions to
this?
Let’s Try a few
3 6x y
5 24 x y
7 76 x y
4 33 x y
Simplifying RadicalsNo denominators with Radicals &
All numbers and exponents in simplest form
List:All perfect squares from
1- 15
All perfect cubes from 1- 6
All perfect fourths from 1- 4
All perfect fifths from 1- 4
Warm-up
42
87
3 4
3 6
3 4
3
44
3
4
50 .9
48 .8
16 .7
40.6
54.5
24.4
8.3
75.2
48.1
yx
yx
x
x
a
x
x
Adding and Subtracting Radicals
must be “like radicals” (same index and radicand)
Examples
3 43 5416.2
273482.1
xx
Rationalizing Denominators &
Numerators
23
7
3 6
3
Ex. 1
Ex. 2
Ex. 3 (with 2 terms in the denominator)
Ex. 4 (with 2 terms in the numerator)
24
3
2
53
Now You Try Some
3 23
823
493
63
4
x
Rational Exponents
n mmn
mnn
m
nn
aaaa
aa
1
1
.2
.1
Examples
2
3
32
53
32
51
532
3 2
100
1 27
32 8
66xx