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Day 1 : Laws of Exponents
ReviewBook sections 7.1 and 7.4
a0 = 1 b-1 = (am)(an) = am + n
= am – n (ab)m = ambm
Do not copy:
Roots and Rational Exponents
If
Then
New Law: Rational Exponents
= 3
Roots and Rational Exponents
If
Then
New Law: Rational Exponents
You may choose whether to find the root
or the power first!
You may choose whether to find the root
or the power first!
Simplify Exponents with Fractions
1.
2.
3.
You try on your marker board
The teacher will show you 10 problems on the smart board. The student will rearrange the form of the equation from:
Exponential to Radical
or
Radical to Exponential
2
1
x
Convert from Exponential to Radical (marker board)
5
2
a
3
1
1
c
3
2
9
2
3
3
x
25 a
31
c 3 c
23 9 3 81
3 327 3 33
33 27
39
33
Everyone to marker board and work with your number partner
c
Convert from Radical to Exponential (marker board)Don’t simplify anything!
3 m
23 4
3 24
23 8
2
1
c
3
1
m
3
2
4
3
2
4
3
2
8
Back to Notes: Simplify ExponentialsAssume all variables are positive
4. 5.
6. 7.
2
7
f
ff 3
3
2
642
3 6424 16
23
3
2
k
k
9
8 2
3
k
k k9
8
103 98 ff
1372 f
2
13f
Simplify Radicals8. 9.
10. 11. 12.
3 125
106425 zyx
5
4
5
5
5
54
3 555
5
5325 zyx 25x
5x
3 756332 rqpm
3 26363 48 rqrqpm
3 222 42 rqqrmp
Practice Laws of Exponents
13. 14.
262
1296
16
8
cba
cba
2
1034 cba
)9(
44
60
m
hg
6
4
9
4
h
m
More Simplifying with exponentsAssume all variables are positive
15. 16.
17. 18.
323
5 32
8
21
x 2
1
1
x
x
1
x
x
x
x
64
3
16
1y
6
4 316
1y
8
6y
5
2
1
32
1
30-60-90 Right Triangle
2x
60°
60°
60°
45-45-90 Right Triangle
X
THEN
49142 xx
1. Simplify 2. Find x 3. Find x 4. Simplify 5. Simplify.
)5()3( 32220 bcba
xq
q
q
2
1
3
7
4 816y
Extra Practice on HW 7.1: Work this out in your math notebook.
Assume all variables are positive.
32
64
49142 xx
1. Simplify 2. Find x 3. Find x 4. Simplify 5. Simplify.
)5()3( 32220 bcba
xq
q
q
2
1
3
7
4 816y
Extra Practice on HW 7.1: Work this out in your math notebook.
Assume all variables are positive.
32
64
22y4
745
c
b
6
11x 16
17x
6. Simplify. 7. Simplify. 8. Simplify. 9. If 4 is the leg of a 45-45-90 triangle, find the other sides.
10. Simplify.
Extra Practice on HW 7.1: Work this out in your math notebook.
Assume all variables are positive.
5
3
3
17
v
3 11554 wx 293
2720
10
5
cb
cba
1
2
1
3
6. Simplify. 7. Simplify. 8. Simplify. 9. If 4 is the leg of a 45-45-90 triangle, find the other sides.
10. Simplify.
Extra Practice on HW 7.1: Work this out in your math notebook.
Assume all variables are positive.
5
3
3
17
v
3 11554 wx 293
2720
10
5
cb
cba
424
1
cb
4.3
5 23
5
17
v
not
vv
or
v
3 223 23 xwxw
424 and3
3
1
2
1
3
HOMEWORK 7.1 due next class!!!
33 Questions