Relax, you aren’t in any trouble. This exponent stuff is a piece of cake. In this activity you...
65
Properties of Exponents
Relax, you aren’t in any trouble. This exponent stuff is a piece of cake. In this activity you will be maneuvering your way through every exponent property
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
Slide 6
Remember, if you are multiplying like bases, we do NOT multiply
the exponents
Slide 7
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
Slide 11
Remember, if you have a power to a power, we do NOT add the
exponents
Slide 12
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 13
Return to The Properties
Slide 14
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?
Slide 23
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?
Slide 28
Return to The Properties
Slide 29
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
Slide 35
Make sure to move the variable and make the exponent POSITIVE
Return to last slide
Slide 36
Return to The Properties Take The Quiz
Slide 37
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
Slide 38
Time to head back and review the property Return to the
property
Slide 39
Return to The Properties
Slide 40
Question #2: (d 6 ) 3 = ? d 63 d9d9 d 18
Slide 41
Time to head back and review the property Return to the
property
Slide 42
Return to The Properties
Slide 43
Question #3: (ab) 5 = ? a5b5a5b5 ab 5 a5ba5b
Slide 44
Time to head back and review the property Return to the
property
Slide 45
Return to The Properties
Slide 46
Question #4: = ? x2x2 x4x4 x 32
Slide 47
Time to head back and review the property Return to the
property
Slide 48
Return to The Properties
Slide 49
Question #5: = ?
Slide 50
Time to head back and review the property Return to the
property
Slide 51
Return to The Properties
Slide 52
Question #6: (97rst) 0 = ? 97 1 0
Slide 53
Time to head back and review the property Return to the
property
Slide 54
Return to The Properties
Slide 55
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
Slide 60
Return to The Properties
Slide 61
Question #9: (x 4 y 5 ) 2 (x 3 y 2 ) 3 = ? x 17 y 16 x 72 y 60
x 36 y 42
Slide 62
Be careful, you are using more than one property at a time here
Return to the problem
Slide 63
Return to The Properties
Slide 64
Question #10: = ?
Slide 65
Be careful, you are using more than one property at a time here
Return to the problem
Slide 66
Congratulations! You really know your exponent properties! Show
Mr. Preiss this screen so can award you full credit for completing
this activity.