Relax, you aren’t in any trouble. This exponent stuff is a piece of cake. In this activity you...
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- Relax, you arent in any trouble. This exponent stuff is a piece
of cake. In this activity you will be maneuvering your way through
every exponent property. In order to advance through the lesson,
you must select the right responses and move ahead to the next
property. If you make a mistake, you will be guided back to the
property to try again. Upon completing every lesson, you will be
required to take a 10 question quiz. Be sure of your answers
though, one slip and you are sent back to the properties and have
to start all over!
- Slide 4
- Product of Powers Power of a Power Power of a Product Quotient
of Powers Zero Exponent Negative Exponents Power of a Quotient
- Slide 5
- Product of Powers When multiplying like bases, we have to ADD
their exponents x m x n = x m+n Example: x 3 x 4 = x 7 Now you
choose the correct answer x 5 x 6 = ? x 30 x 56 x 11
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- Remember, if you are multiplying like bases, we do NOT multiply
the exponents
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- Notice if we were to break up the previous problem as the
following x 5 x 6 = ? x x x x x x x x x x x Since x 5 means x times
itself five times and x 6 means x times itself six times. How many
of the x times itself did we end up with?
- Slide 8
- Return to The Properties
- Slide 9
- Notice if we were to break up the previous problem as the
following x 5 x 6 = ? x x x x x x x x x x x Since x 5 means x times
itself five times and x 6 means x times itself six times. How many
of the x times itself did we end up with?
- Slide 10
- Power of a Power When a base with a power is raised to another
power, we MULTIPLY their exponents (x m ) n = x m n Example: (x 2 )
8 = x 16 Now you choose the correct answer (x 3 ) 4 = ? x 12 x 34
x7x7
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- Remember, if you have a power to a power, we do NOT add the
exponents
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- Now if we were to break up the previous problem as the
following (x 3 ) 4 = ? (x x x) 4 And continued to break these up
using the ideas from the first property, we could get (x x x) (x x
x) How many of the x times itself did we end up with?
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- Return to The Properties
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- Now if we were to break up the previous problem as the
following (x 3 ) 4 = ? (x x x) 4 And continued to break these up
using the ideas from the first property, we could get (x x x) (x x
x) How many of the x times itself did we end up with?
- Slide 15
- Power of a Product When a product is raised to a power,
EVERYTHING in the product receives that power (xy) m = x m y m
Example: (xy) 7 = x 7 y 7 Now you choose the correct answer (xy) 2
= ? x2yx2yx2y2x2y2 xy 2
- Slide 16
- Remember, if you have a product to a power, ALL terms must
receive that power
- Slide 17
- Now if we were to break up the previous problem as the
following (xy) 2 = ? (xy) And thinking about what happens when we
multiply like bases, what would the powers of each variable
be?
- Slide 18
- Return to The Properties
- Slide 19
- Now if we were to break up the previous problem as the
following (xy) 2 = ? (xy) And thinking about what happens when we
multiply like bases, what would the powers of each variable
be?
- Slide 20
- Quotient of Powers When dividing like bases, we have to
SUBTRACT their exponents = x m-n Example: = x 6 Now you choose the
correct answer = ? x8x8 x2x2 x 24
- Slide 21
- Remember, if you are dividing like bases, do NOT divide their
exponents
- Slide 22
- Now if we were to break up the previous problem as the
following Looking at the xs in the numerator and the denominator.
If every x in the numerator was cancelled by one in the
denominator, how many of the x times themselves would be left and
where would they be?
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- Return to The Properties
- Slide 24
- Now if we were to break up the previous problem as the
following Looking at the xs in the numerator and the denominator.
If every x in the numerator was cancelled by one in the
denominator, how many of the x times themselves would be left and
where would they be?
- Slide 25
- Power of a Quotient When a quotient is raised to a power,
EVERYTHING in the quotient gets that power = Example: = Now you
choose the correct answer = ?
- Slide 26
- Remember, if you have a quotient to a power, ALL terms receive
that power
- Slide 27
- Now if we were to break up the previous problem as the
following Looking at the xs being multiplied in the numerator and
the ys being multiplied in the denominator, how many of the x times
themselves are in the numerator and how many of the y times
themselves are in the denominator?
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- Return to The Properties
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- Now if we were to break up the previous problem as the
following Looking at the xs being multiplied in the numerator and
the ys being multiplied in the denominator, how many of the x times
themselves are in the numerator and how many of the y times
themselves are in the denominator?
- Slide 30
- Zero Exponent Anything to the power of zero is ALWAYS equal to
one x 0 = 1 Example: (4xy) 0 = 1 Now you choose the correct answer
(9x 5 yz 17 ) 0 = ? 1 0 x
- Slide 31
- Remember, if anything has zero as an exponent, that does NOT
mean it equals zero Return to last slide
- Slide 32
- Return to The Properties
- Slide 33
- For a brief look at why anything to the power of zero is one,
take a look at a few explanations here.here
- Slide 34
- Negative Exponents We can never have a negative exponent, so if
we have one we have to MOVE the base to make it positive. If it is
on top it goes to the bottom, if it is on bottom it goes to the
top.x -m =or= x m Example: = x 4 Now you choose the correct answer
x -3 -x 3
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- Make sure to move the variable and make the exponent POSITIVE
Return to last slide
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- Return to The Properties Take The Quiz
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- Simplify the following quiz questions using the properties of
exponents that you have learned in the activity. Question #1: y 4 y
5 = ? y 20 y9y9 y 45
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- Time to head back and review the property Return to the
property
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- Return to The Properties
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- Question #2: (d 6 ) 3 = ? d 63 d9d9 d 18
- Slide 41
- Time to head back and review the property Return to the
property
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- Return to The Properties
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- Question #3: (ab) 5 = ? a5b5a5b5 ab 5 a5ba5b
- Slide 44
- Time to head back and review the property Return to the
property
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- Return to The Properties
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- Question #4: = ? x2x2 x4x4 x 32
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- Time to head back and review the property Return to the
property
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- Return to The Properties
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- Question #5: = ?
- Slide 50
- Time to head back and review the property Return to the
property
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- Return to The Properties
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- Question #6: (97rst) 0 = ? 97 1 0
- Slide 53
- Time to head back and review the property Return to the
property
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- Return to The Properties
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- Question #7: = ? a6a6 -a 6 a -6
- Slide 56
- Time to head back and review the property Return to the
property
- Slide 57
- Return to The Properties
- Slide 58
- Question #8: (x 2 y 3 ) 4 = ? x6y7x6y7 xy 9 x 8 y 12
- Slide 59
- Be careful, you are using more than one property at a time here
Return to the problem
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- Return to The Properties
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- Question #9: (x 4 y 5 ) 2 (x 3 y 2 ) 3 = ? x 17 y 16 x 72 y 60
x 36 y 42
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- Be careful, you are using more than one property at a time here
Return to the problem
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- Return to The Properties
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- Question #10: = ?
- Slide 65
- Be careful, you are using more than one property at a time here
Return to the problem
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- Congratulations! You really know your exponent properties! Show
Mr. Preiss this screen so can award you full credit for completing
this activity.