exponent laws: an investigation
DESCRIPTION
Exponent Laws: An Investigation. 1 st Law : Product of Powers. Write the expanded form of the first product in the table. 1 st Law : Product of Powers. Write the expanded form of the first product in the table. 1 st Law : Product of Powers. Now write it as a single power. - PowerPoint PPT PresentationTRANSCRIPT
Exponent Laws:An Investigation
Write the expanded form of the first product in the table.
1st Law: Product of Powers
Product Expanded Form Single Power
23 x 24
52 x 51
32 x 33 x 3
p5 x p2
g3 x g x g4
Write the expanded form of the first product in the table.
1st Law: Product of Powers
Product Expanded Form Single Power
23 x 24 2x2x2 x 2x2x2x2
52 x 51
32 x 33 x 3
p5 x p2
g3 x g x g4
Now write it as a single power.
1st Law: Product of Powers
Product Expanded Form Single Power
23 x 24 2x2x2 x 2x2x2x2
52 x 51
32 x 33 x 3
p5 x p2
g3 x g x g4
Now write it as a single power.
1st Law: Product of Powers
Product Expanded Form Single Power
23 x 24 2x2x2 x 2x2x2x2 27
52 x 51
32 x 33 x 3
p5 x p2
g3 x g x g4
Repeat the previous two instructions for the remaining products in the table.
1st Law: Product of Powers
Product Expanded Form Single Power
23 x 24 2x2x2 x 2x2x2x2 27
52 x 51
32 x 33 x 3
p5 x p2
g3 x g x g4
Repeat the previous two instructions for the remaining products in the table.
1st Law: Product of Powers
Product Expanded Form Single Power
23 x 24 2x2x2 x 2x2x2x2 27
52 x 51 5x5 x 5
32 x 33 x 3
p5 x p2
g3 x g x g4
Repeat the previous two instructions for the remaining products in the table.
1st Law: Product of Powers
Product Expanded Form Single Power
23 x 24 2x2x2 x 2x2x2x2 27
52 x 51 5x5 x 5 53
32 x 33 x 3
p5 x p2
g3 x g x g4
Repeat the previous two instructions for the remaining products in the table.
1st Law: Product of Powers
Product Expanded Form Single Power
23 x 24 2x2x2 x 2x2x2x2 27
52 x 51 5x5 x 5 53
32 x 33 x 3 3x3 x 3x3x3 x 3
p5 x p2
g3 x g x g4
Repeat the previous two instructions for the remaining products in the table.
1st Law: Product of Powers
Product Expanded Form Single Power
23 x 24 2x2x2 x 2x2x2x2 27
52 x 51 5x5 x 5 53
32 x 33 x 3 3x3 x 3x3x3 x 3 36
p5 x p2
g3 x g x g4
Repeat the previous two instructions for the remaining products in the table.
1st Law: Product of Powers
Product Expanded Form Single Power
23 x 24 2x2x2 x 2x2x2x2 27
52 x 51 5x5 x 5 53
32 x 33 x 3 3x3 x 3x3x3 x 3 36
p5 x p2 pxpxpxpxp x pxp
g3 x g x g4
Repeat the previous two instructions for the remaining products in the table.
1st Law: Product of Powers
Product Expanded Form Single Power
23 x 24 2x2x2 x 2x2x2x2 27
52 x 51 5x5 x 5 53
32 x 33 x 3 3x3 x 3x3x3 x 3 36
p5 x p2 pxpxpxpxp x pxp p7
g3 x g x g4
Repeat the previous two instructions for the remaining products in the table.
1st Law: Product of Powers
Product Expanded Form Single Power
23 x 24 2x2x2 x 2x2x2x2 27
52 x 51 5x5 x 5 53
32 x 33 x 3 3x3 x 3x3x3 x 3 36
p5 x p2 pxpxpxpxp x pxp p7
g3 x g x g4 gxgxg x g x gxgxgxg
Repeat the previous two instructions for the remaining products in the table.
1st Law: Product of Powers
Product Expanded Form Single Power
23 x 24 2x2x2 x 2x2x2x2 27
52 x 51 5x5 x 5 53
32 x 33 x 3 3x3 x 3x3x3 x 3 36
p5 x p2 pxpxpxpxp x pxp p7
g3 x g x g4 gxgxg x g x gxgxgxg g8
What pattern can be seen?
In General:When multiplying powers with the same base, keep the base and add the exponents.
y a y b y ab
2nd Law: Quotient of Powers
Quotient Expanded Form Single Power
85 83
64 61
96 95
p5 p2
g3 g
For each quotient, write both its parts in expanded form and then as a single power.
2nd Law: Quotient of Powers
Quotient Expanded Form Single Power
85 83
64 61
96 95
p5 p2
g3 g
For each quotient, write both its parts in expanded form and then as a single power.
88888888
2nd Law: Quotient of Powers
Quotient Expanded Form Single Power
85 83
64 61
96 95
p5 p2
g3 g
For each quotient, write both its parts in expanded form and then as a single power.
88888888
82
2nd Law: Quotient of Powers
Quotient Expanded Form Single Power
85 83
64 61
96 95
p5 p2
g3 g
For each quotient, write both its parts in expanded form and then as a single power.
88888888
82
66666
2nd Law: Quotient of Powers
Quotient Expanded Form Single Power
85 83
64 61
96 95
p5 p2
g3 g
For each quotient, write both its parts in expanded form and then as a single power.
88888888
82
66666
63
2nd Law: Quotient of Powers
Quotient Expanded Form Single Power
85 83
64 61
96 95
p5 p2
g3 g
For each quotient, write both its parts in expanded form and then as a single power.
88888888
82
66666
63
99999999999
2nd Law: Quotient of Powers
Quotient Expanded Form Single Power
85 83
64 61
96 95
p5 p2
g3 g
For each quotient, write both its parts in expanded form and then as a single power.
88888888
82
66666
63
99999999999
91
2nd Law: Quotient of Powers
Quotient Expanded Form Single Power
85 83
64 61
96 95
p5 p2
g3 g
For each quotient, write both its parts in expanded form and then as a single power.
88888888
82
66666
63
99999999999
91
ppppppp
2nd Law: Quotient of Powers
Quotient Expanded Form Single Power
85 83
64 61
96 95
p5 p2
g3 g
For each quotient, write both its parts in expanded form and then as a single power.
88888888
82
66666
63
99999999999
91
ppppppp
p3
2nd Law: Quotient of Powers
Quotient Expanded Form Single Power
85 83
64 61
96 95
p5 p2
g3 g
For each quotient, write both its parts in expanded form and then as a single power.
88888888
82
66666
63
99999999999
91
ppppppp
p3
gggg
2nd Law: Quotient of Powers
Quotient Expanded Form Single Power
85 83
64 61
96 95
p5 p2
g3 g
For each quotient, write both its parts in expanded form and then as a single power.
88888888
82
66666
63
99999999999
91
ppppppp
p3
gggg
g2
What pattern can be seen?
In General:When dividing powers with the same base, keep the base and subtract the exponents.
y a y b y a b
3rd Law: Powers of Powers
Power of a Power Expanded Form Single Power
43 2
72 4
y 4 3
Write each power of a power in expanded form and then as a single power.
3rd Law: Powers of Powers
Power of a Power Expanded Form Single Power
43 2
72 4
y 4 3
Write each power of a power in expanded form and then as a single power.
43 43 444444
3rd Law: Powers of Powers
Power of a Power Expanded Form Single Power
43 2
72 4
y 4 3
Write each power of a power in expanded form and then as a single power.
43 43 444444
46
3rd Law: Powers of Powers
Power of a Power Expanded Form Single Power
43 2
72 4
y 4 3
Write each power of a power in expanded form and then as a single power.
43 43 444444
46
72 72 72 72 77777777
3rd Law: Powers of Powers
Power of a Power Expanded Form Single Power
43 2
72 4
y 4 3
Write each power of a power in expanded form and then as a single power.
43 43 444444
46
72 72 72 72 77777777
78
3rd Law: Powers of Powers
Power of a Power Expanded Form Single Power
43 2
72 4
y 4 3
Write each power of a power in expanded form and then as a single power.
43 43 444444
46
72 72 72 72 77777777
78
y 4 y 4 y 4 yyyyyyyyyyyy
3rd Law: Powers of Powers
Power of a Power Expanded Form Single Power
43 2
72 4
y 4 3
Write each power of a power in expanded form and then as a single power.
43 43 444444
46
72 72 72 72 77777777
78
y 4 y 4 y 4 yyyyyyyyyyyy
y12
What pattern can be seen?
In General:When writing a power of a power as a single power, keep the base and multiply the exponents.
y a b y ab
Try a few examples…
Write each as a single power, then evaluate using a calculator.
34 32
58 55
23 3a) b) c)
Write each as a single power, then evaluate using a calculator.
34 32
58 55
23 3a) b) c)
36
Write each as a single power, then evaluate using a calculator.
34 32
58 55
23 3a) b) c)
36
729
Write each as a single power, then evaluate using a calculator.
34 32
58 55
23 3a) b) c)
36
729
53
Write each as a single power, then evaluate using a calculator.
34 32
58 55
23 3a) b) c)
36
729
53
125
Write each as a single power, then evaluate using a calculator.
34 32
58 55
23 3a) b) c)
36
729
53
125
29
Write each as a single power, then evaluate using a calculator.
34 32
58 55
23 3a) b) c)
36
729
53
125
29
512
Now try these…
Simplify.
x 3 x 4 x 5
r19 r8
b12 3a) b) c)
Simplify.
x 3 x 4 x 5
r19 r8
b12 3a) b) c)
x 345
Simplify.
x 3 x 4 x 5
r19 r8
b12 3a) b) c)
x 345
x12
Simplify.
x 3 x 4 x 5
r19 r8
b12 3a) b) c)
x 345
x12
r19 8
Simplify.
x 3 x 4 x 5
r19 r8
b12 3a) b) c)
x 345
x12
r19 8
r11
Simplify.
x 3 x 4 x 5
r19 r8
b12 3a) b) c)
x 345
x12
r19 8
r11
b123
Simplify.
x 3 x 4 x 5
r19 r8
b12 3a) b) c)
x 345
x12
r19 8
r11
b123
b36
Now try a few tricky ones…
Simplify.
a) b)
xy 3 2x 5y 6
12x 7y 2
2xy 3
xy 3
3x
Simplify.
a) b)
xy 3 2x 5y 6
12x 7y 2
2xy 3
xy 3
3x
1xy 3 2x 5y 6
Simplify.
a) b)
xy 3 2x 5y 6
12x 7y 2
2xy 3
xy 3
3x
1xy 3 2x 5y 6
12x1 x 5 y 3 y 6
Simplify.
a) b)
xy 3 2x 5y 6
12x 7y 2
2xy 3
xy 3
3x
1xy 3 2x 5y 6
12x1 x 5 y 3 y 6
2x 6y 9
Simplify.
a) b)
xy 3 2x 5y 6
12x 7y 2
2xy 3
xy 3
3x
1xy 3 2x 5y 6
12x1 x 5 y 3 y 6
2x 6y 9
12x 7y 2
2xy 2xy 2xy xy 3
3x
Simplify.
a) b)
xy 3 2x 5y 6
12x 7y 2
2xy 3
xy 3
3x
1xy 3 2x 5y 6
12x1 x 5 y 3 y 6
2x 6y 9
12x 7y 2
2xy 2xy 2xy xy 3
3x
12x 7y 2
2 2 2 x x x y y y xy 3
3x
Simplify.
a) b)
xy 3 2x 5y 6
12x 7y 2
2xy 3
xy 3
3x
1xy 3 2x 5y 6
12x1 x 5 y 3 y 6
2x 6y 9
12x 7y 2
2xy 2xy 2xy xy 3
3x
12x 7y 2
2 2 2 x x x y y y xy 3
3x
12x 7y 2
8x 3y 3
xy 3
3x
Simplify.
a) b)
xy 3 2x 5y 6
12x 7y 2
2xy 3
xy 3
3x
1xy 3 2x 5y 6
12x1 x 5 y 3 y 6
2x 6y 9
12x 7y 2
2xy 2xy 2xy xy 3
3x
12x 7y 2
2 2 2 x x x y y y xy 3
3x
12x 7y 2
8x 3y 3
xy 3
3x
12 1 x 7 x y 2 y 3
8 3 x 3 x y 3
Simplify.
a) b)
xy 3 2x 5y 6
12x 7y 2
2xy 3
xy 3
3x
1xy 3 2x 5y 6
12x1 x 5 y 3 y 6
2x 6y 9
12x 7y 2
2xy 2xy 2xy xy 3
3x
12x 7y 2
2 2 2 x x x y y y xy 3
3x
12x 7y 2
8x 3y 3
xy 3
3x
12 1 x 7 x y 2 y 3
8 3 x 3 x y 3
12x 8y 5
24x 4y 3
Simplify.
a) b)
xy 3 2x 5y 6
12x 7y 2
2xy 3
xy 3
3x
1xy 3 2x 5y 6
12x1 x 5 y 3 y 6
2x 6y 9
12x 7y 2
2xy 2xy 2xy xy 3
3x
12x 7y 2
2 2 2 x x x y y y xy 3
3x
12x 7y 2
8x 3y 3
xy 3
3x
12 1 x 7 x y 2 y 3
8 3 x 3 x y 3
12x 8y 5
24x 4y 3
x 4y 2
2