Exponents in Action (Video)

1
Base Camp
Exponents in Action (Video)
Id rather read about it ?
Listen and see!
Short and sweet- Summary of rules
To the Laws!
Lets Play!
Practice makes perfect!
Quiz Me!
Sing me the rules
2
Video
Introducing Exponents

1. Click on the link above. You will be taken to a
   blog about introducing exponents.
2. In the first paragraph, there is a link to an
   algebra lesson by NROC Algebra 1An Open course,
   Unit 7, Lesson 1, Topic 1 Rules of Exponents.
   Click on the link.
3. Click on LOG IN AS GUEST.
4. On the new webpage, click on the PRESENTATION
   link.

3
Practice makes perfect!
Introducing Exponents

1. Click on the link above. You will be taken to a
   blog about introducing exponents.
2. In the first paragraph, there is a link to an
   algebra lesson by NROC Algebra 1An Open course,
   Unit 7, Lesson 1, Topic 1 Rules of Exponents.
   Click on the link.
3. Click on LOG IN AS GUEST.
4. On the new webpage, click on the WORKED EXAMPLES
   link.
5. After viewing the examples, click on the PRACTICE
   link.

4
Listen and See
Exponent Tutorials
Click on the above link to visit a webpage with
various tutorials about the different laws of
exponents. Explore any or all of them for better
understanding!
5
Exponent Game
Exponent Battleship
6
Exponent Song
Sing me the Rules!
7
Reading
Let's Learn the Exponential Laws
8
Quiz Me!
Quiz 1
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Laws of Exponents
Law 1
Law 4
Law 7
Law 2
Law 5
Law 8
Law 3
Law 6
Law 9
10
Law 1
Any number raised to the power of 1 equals itself.
x1 x
Show me more!
Back to the laws!
11
Law 1 - examples
x1 x
101 10 61 6 1291 129 31 3 z1 z b1
b y1 y t1 t
Back to the laws!
12
My turn to practice.
Law x1 x
Q1 81 ?
1
9
8
7
Back to the laws!
13
Great job! You did it!
Thats right! Any number raised to the power of
one is itself, so 81 8.
On to the next problem!
Back to the laws!
14
My turn to practice.
Law x1 x
Q2 r1 ?
s
r
1
t
Back to the laws!
15
Super!
Thats right! Any number raised to the power of
one is itself, so r1 r.
Back to the laws!
On to the next law!
16
Oops! Try again!
Remember, any number raised to the power of one
is itself!
Back to the problem!
17
Law 2
Any number (except 0) raised to the power of 0
equals 1.
x0 1
Show me more!
Back to the laws!
18
Law 2 - examples
x0 1
100 1 60 1 1290 1 30 1 z0 1 b0 1 y0
1 t0 1
Back to the laws!
19
My turn to practice.
Law x0 1
Q1 80 ?
1
0
8
80
Back to the laws!
20
Yay!
Thats right! Any number raised to the power of
zero is 1, so 80 1.
On to the next problem!
Back to the laws!
21
My turn to practice.
Law x0 1
Q2 t0 ?
s
10
t
1
Back to the laws!
22
Good job!
Thats right! Any number raised to the power of
zero is 1, so t0 1.
Back to the laws!
On to the next law!
23
Not yet! Try again!
Remember, any number raised to the power of zero
is 1.
Back to the problem!
24
Law 3
Any number raised to the power of -1 equals its
reciprocal (multiplicative inverse).
x-1 1/x where x ? 0
Show me more!
Back to the laws!
25
Law 3 - examples
x-1 1/x where x ? 0
10-1 1/10 6-1 1/6 129-1 1/129 3-1 1/3 z-1
1/z b-1 1/b y-1 1/y t-1 1/t
Back to the laws!
26
My turn to practice.
Law x-1 1/x
Q1 4-1 ?
41
1/4
14
-4
Back to the laws!
27
You did it!
Thats right! Any number raised to the power of
-1 is 1 over itself (its reciprocal), so 4-1
1/4.
On to the next problem!
Back to the laws!
28
My turn to practice.
Law x-1 1/x
Q2 z-1 ?
z
z/z
-z
1/z
Back to the laws!
29
Looking good!
Thats right! Any number raised to the power of
-1 is one over itself (its reciprocal), so z-1
1/z.
Back to the laws!
On to the next law!
30
Think again!
Remember, any number raised to the power of -1 is
1 over itself (its reciprocal).
Back to the problem!
31
Law 4
Any number raised to a power multiplied by that
same number raised to another power equals the
same number raised to the sum of the powers.
xmxn xmn
Show me more!
Back to the laws!
32
Law 4 - examples
xmxn xmn
104105 109 6367 610 12921295 1297 3638
314 x5x8 x13 b2b4 b6 y1y4 y5 t2t3 t5
Back to the laws!
33
My turn to practice.
Law xmxn xmn
Q1 5258 ?
510
1028
1010
2510
Back to the laws!
34
Yippee!
Thats right! Any number raised to a power
multiplied by the same number raised to another
power is equal to that same number raised to the
sum of the powers. So, 5258 510
On to the next problem!
Back to the laws!
35
My turn to practice.
Law xmxn xmn
Q2 v3v6 ?
v18
v9
v3
v36
Back to the laws!
36
Not quite!
Remember, any number raised to a power multiplied
by the same number raised to another power is
equal to that same number raised to the sum of
the powers.
Back to the problem!
37
Couldnt be better!
Thats right! Any number raised to a power
multiplied by the same number raised to another
power is equal to that same number raised to the
sum of the powers. So, v3v6 v9
Back to the laws!
On to the next law!
38
Law 5
Any number raised to a power divided by that same
number raised to another power equals the same
number raised to the difference of the powers.
xm/xn xm-n
Show me more!
Back to the laws!
39
Law 5 - examples
xm/xn xm-n
107/105 102 63/61 62 1294/1292 1292 39/35
34 x9/x2 x7 b6/b3 b3 y8/y4 y4 t9/t3 t6
Back to the laws!
40
My turn to practice.
Law xm/xn xm-n
Q1 57/54 ?
511
103
574
53
Back to the laws!
41
You are so right!
Thats right! Any number raised to a power
divided by the same number raised to another
power is equal to that same number raised to the
difference of the powers. So, 57/54 53
On to the next problem!
Back to the laws!
42
My turn to practice.
Law xm/xn xm-n
Q2 v8/v6 ?
v86
v14
v2
v10
Back to the laws!
43
Lets try that again!
Remember, any number raised to a power divided by
the same number raised to another power is equal
to that same number raised to the difference of
the powers.
Back to the problem!
44
Wow!
Thats right! Any number raised to a power
divided by the same number raised to another
power is equal to that same number raised to the
difference of the powers. So, v8/v6 v2
Back to the laws!
On to the next law!
45
Law 6
Any number raised to a power then raised to
another power equals the same number raised to
the product of the powers.
(xm)n xmn
Show me more!
Back to the laws!
46
Law 6 - examples
(xm)n xmn
(107)5 1035 (63)4 612 (1292)5 12910 (36)8
348 (x2)7 x14 (b3)5 b15 (y7)3 y21 (t9)1
t9
Back to the laws!
47
My turn to practice.
Law (xm)n xmn
Q1 (57)3 ?
510
353
521
157
Back to the laws!
48
Youve got it!
Thats right! Any number raised to a power then
raised to another power is that same number
raised to the product of the powers. So, (57)3
521
On to the next problem!
Back to the laws!
49
My turn to practice.
Law (xm)n xmn
Q2 (v4)8 ?
v48
v4
v12
v32
Back to the laws!
50
Sorry!
Remember, any number raised to a power then
raised to another power is equal to that same
number raised to the product of the powers.
Back to the problem!
51
Nice work!
Thats right! Any number raised to a power then
raised to another power is that same number
raised to the product of the powers. So, (v4)8
v32
Back to the laws!
On to the next law!
52
Law 7
Any product of two numbers raised to a power
equals the first number raised to the power
multiplied by the second number raised to the
same power.
(xy)n xnyn
Show me more!
Back to the laws!
53
Law 7 - examples
(xy)n xnyn
(103)5 10535 (62)3 6323 (127)2
12272 (45)4 4454 (xz)4 x4z4 (bc)3
b3c3 (rs)7 r7s7 (tu)6 t6u6
These numerical expressions can be simplified
to a whole number.
Back to the laws!
54
My turn to practice.
Law (xy)n xnyn
Q1 (53)7 ?
5737
573
537
157
Back to the laws!
55
Thats it!
Thats right! Any product of two numbers raised
to a power equals the first number raised to the
power multiplied by the second number raised to
the same power. So, (53)7 5737
On to the next problem!
Back to the laws!
56
My turn to practice.
Law (xy)n xnyn
Q2 (vt)8 ?
8vt
v8t8
vt8
v8t
Back to the laws!
57
Lets go back!
Remember, any product of two numbers raised to a
power equals the first number raised to the power
multiplied by the second number raised to the
same power.
Back to the problem!
58
Youre doing great!
Thats right! Any product of two numbers raised
to a power equals the first number raised to the
power multiplied by the second number raised to
the same power. So, (vt)8 v8t8
Back to the laws!
On to the next law!
59
Law 8
Any quotient raised to a power equals the first
number raised to the power divided by the second
number raised to the power.
(x/y)n xn/yn Where y ? 0
Show me more!
Back to the laws!
60
Law 8 - examples
(x/y)n xn/yn Where y ? 0
(10/3)5 105/35 (6/2)3 63/23 (12/7)2
122/72 (4/5)4 44/54 (x/z)4 x4/z4 (b/c)3
b3/c3 (r/s)7 r7/s7 (t/u)6 t6/u6
Back to the laws!
61
My turn to practice.
Law (x/y)n xn/yn
Q1 (6/4)3 ?
6/43
6/12
63/43
63/4
Back to the laws!
62
Nice work!
Thats right! Any quotient raised to a power
equals the first number raised to the power
divided by the second number raised to the
power. So, (6/4)3 63/43
On to the next problem!
Back to the laws!
63
My turn to practice.
Law (x/y)n xn/yn
Q2 (v/t)7 ?
v7t7
v7/t7
7vt
v7t
Back to the laws!
64
Try again!
Remember, any quotient raised to a power equals
the first number raised to the power divided by
the second number raised to the power.
Back to the problem!
65
Super!
Thats right! Any quotient raised to a power
equals the first number raised to the power
divided by the second number raised to the
power. So, (v/t)7 v7/t7
Back to the laws!
On to the next law!
66
Law 9
Any number raised to a negative power equals one
over the number raised to the power.
x-n 1/xn
Show me more!
Back to the laws!
67
Law 9 - examples
x-n 1/xn
10-5 1/105 6-4 1/64 12-3 1/123 4-7
1/47 x-8 1/x8 b-5 1/b5 r-2 1/r2 t-7 1/t7
Back to the laws!
68
My turn to practice.
Law x-n 1/xn
Q1 8-3 ?
1/83
1/24
1/83
83
Back to the laws!
69
Nice job!
Thats right! Any number raised to a negative
power equals one over the number raised to the
power. So, 8-3 1/83
On to the next problem!
Back to the laws!
70
My turn to practice.
Law x-n 1/xn
Q2 t-9 ?
1/9t
t9
9t
1/t9
Back to the laws!
71
Not yet, try again!
Remember, any number raised to a negative power
equals one over the number raised to the power.
Back to the problem!
72
Terrific!
Thats right! Any number raised to a negative
power equals one over the number raised to the
power. So, t-9 1/t9
Back to the laws!
73
In summary
x1 x x0 1 x-1 1/x xmxn xmn xm/xn
xm-n (xm)n xmn (xy)n xnyn (x/y)n xn/yn x-n
1/xn