Bell Ringer
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Transcript of Bell Ringer
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Bell Ringer
2. 7(x + 3)= 105 7x + 21 = 105 -21 -21 7x = 84 7 7 x = 12
Solve.1. 5x + 18 = -3x – 14 +3x +3x 8x + 18 = -14
- 18 -18 8x = -32
8 8 x = -4
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Quiz Results
Since there are still a few who haven’t taken the quiz, I’ll give out the results as soon as they do.
If you want to know your grade, log onto your Gradebook and check it yourself.
Otherwise, you’ll have to wait… NO, I’m not digging through the papers
to tell you your grade.
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Exponents and Radicals
NCP 503: Work with numerical factorsNCP 505: Work with squares and square roots of numbersNCP 506: Work problems involving positive integer exponents*NCP 504: Work with scientific notationNCP 507: Work with cubes and cube roots of numbersNCP 604: Apply rules of exponents
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Basic Terminology
34
Exponent
Base
= 3•3•3•3 = 81
The base is multiplied by itself the same number of times as the exponent calls for.
Its read, “Three to the fourth power.”
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Important Examples
-34 = –(3•3•3•3) = -81
(-3)4 = (-3)•(-3)•(-3)•(-3) = 81
(-3)3 = (-3)•(-3)•(-3) = -27
-33 = –(3•3•3) = -27
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Variable Expressions
x4 = x • x • x • x y3 = y • y • y
Evaluate each expression if x = 2 and y = 5
x4 y2 = (2•2•2•2)•(5•5) = 4003xy3 = 3•2•(5•5•5)
= 750
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Zero Exponent PropertyNegative Exponent Property
Product of PowersQuotient of Powers
Laws of Exponents, Pt. I
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Zero Exponent Property
Any number or variable raised to the zero power is 1.
x0 = 1 y0 = 1 z0 = 1
70 = 1 -540 = 1 1230 = 1
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Negative Exponent
Any number raised to a negative exponent is the reciprocal of the number.
x-1 = y-1 = 5-1 =
x-2 = 3-2 = = 5-3 = =
1X
1y
15
1X2
132
19
153
1 .125
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Negative Exponent
3x-3 = 5y-2 =
2x-2 y2= 3-2 x4=
3x3
5y2
2y2
x2 x4
32
Only x is raised to the -3 power!
Only x is on the bottom.
x4
9 =
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Product of Powers
This property is used to combine 2 or more exponential expressions with the SAME base.
53•52 = (5•5•5)•(5•5)
= 55
If the bases are the same, add the exponent!
x4•x3 = (x•x•x•x)•(x•x•x) = x7
Multiplication NOT Addition!
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Product of Powers
6-2•6-3
=
165
162•63
=
=
17776
x-5•x-7
=
1x12
1x5•x7
=
n-3•n5 =
n2 n-3+5 =
Product of powers also work with negative exponents!
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Quotient of Powers
This property is used when dividing two or more exponential expressions with the
same base.
x6
x3= x6-
3
= x3
Subtract the exponents! (Top minus the bottom!)
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Quotient of Powers
67
65= 67-
5
= 62
x3
x5= x3-
5
= x-2 =
1x2
x3
x5= x ∙ x ∙
xx∙x∙x∙x∙x
=OR
1x2
= 36
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Laws of Exponents, Pt. II
Power of a PowerPower of a ProductPower of a Quotient
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Power of a Power
This property is used to write an exponential expression as a single power of the base.
(63)4 = 63•63•63•63
= 612
When you have an exponent raised to an exponent, multiply the
exponents!
(x5)3 = x5•x5•x5 = x15
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Power of a Power
(54)8 = 532
(n3)4 = n12
(3-2)-3 = 36
(x5)-3 = x-15
Multiply the exponents!
= 1x15
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Power of a Product
(xy)3
(2x)5
(xyz)4
Power of a Product – Distribute the exponent on the outside of the parentheses to all of the terms inside of the parentheses.
= x3y3
= 25 ∙ x5
= 32x5
= x4 y4 z4
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Power of a Product
(x3y2)3
(3x2)4
(3xy)2
More examples…
= x9y6
= 34 ∙ x8
= 81x8
= 32 ∙ x2 ∙ y2
= 9x2y2
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Power of a Quotient
Power of a Quotient – Distribute the exponent on the outside of the parentheses to the numerator and the denominator of the fraction.
xy
=( )5 x5
y5( )
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Power of a Quotient
More examples…
2x
=( )3 23
x3( )=8x3
3x2y
=( )4 34
x8y4( )= 81x8y4
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Basic Examples
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Basic Examples 32 xx 32x 5x
34x 34x 12x
3xy 33yx
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3
y
x3
3
y
x
4
7
x
x 3x
7
5
x
x2
1
x
Basic Examples
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More Difficult Examples
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More Examples
43 72 aa 4372 a 714a
232 285 rrr 232285 r 780r
33xy 3333 yx 3327 yx
2
3
2
b
a
22
22
3
2
b
a2
2
9
4
b
a
3522 nm 3532312 nm 15632 nm 1568 nm
x
x
2
8 4
12
8 14x 34x
5
3
3
9
z
z 35
1
3
9
z
2
13x 2
3
x
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More Examples
223 73 xyzzyx 21121373 zyx 33421 zyx
32 238 xyxyxy 312111238 yx 6348 yx
22232 23 xyyx 222121232221 23 yxyx
4264 49 yxyx 462449 yx 10636 yx
3
2
3
3
5
ab
ba
323131
313331
3
5
ba
ba
633
393
3
5
ba
ba
63
39
27
125
ba
ba
36
39
27
125
b
a3
6
27
125
b
a