Mr. Preiss Algebra 1 Relax, you aren’t in any trouble. This exponent stuff is a piece of cake. In...
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Properties of Exponents Mr. Preiss Algebra 1
Mr. Preiss Algebra 1 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
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 Return to last slide
Slide 7
Return to The Properties
Slide 8
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 9
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 10
Remember, if you have a power to a power, we do NOT add the
exponents Return to last slide
Slide 11
Return to The Properties
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
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 14
Remember, if you have a product to a power, ALL terms must
receive that power Return to last slide
Slide 15
Return to The Properties
Slide 16
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 17
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 18
Remember, if you are dividing like bases, do NOT divide their
exponents Return to last slide
Slide 19
Return to The Properties
Slide 20
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 21
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 22
Remember, if you have a quotient to a power, ALL terms receive
that power Return to last slide
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 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 25
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 26
Remember, if anything has zero as an exponent, that does NOT
mean it equals zero Return to last slide
Slide 27
Return to The Properties
Slide 28
For a brief look at why anything to the power of zero is one,
take a look at a few explanations here.here
Slide 29
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 30
Make sure to move the variable and make the exponent POSITIVE
Return to last slide
Slide 31
Return to The Properties Take The Quiz
Slide 32
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 33
Time to head back and review the property Return to the
property
Slide 34
Return to The Properties
Slide 35
Question #2: (d 6 ) 3 = ? d 63 d9d9 d 18
Slide 36
Time to head back and review the property Return to the
property
Slide 37
Return to The Properties
Slide 38
Question #3: (ab) 5 = ? a5b5a5b5 ab 5 a5ba5b
Slide 39
Time to head back and review the property Return to the
property
Slide 40
Return to The Properties
Slide 41
Question #4: = ? x2x2 x4x4 x 32
Slide 42
Time to head back and review the property Return to the
property
Slide 43
Return to The Properties
Slide 44
Question #5: = ?
Slide 45
Time to head back and review the property Return to the
property
Slide 46
Return to The Properties
Slide 47
Question #6: (97rst) 0 = ? 97 1 0
Slide 48
Time to head back and review the property Return to the
property
Slide 49
Return to The Properties
Slide 50
Question #7: = ? a6a6 -a 6 a -6
Slide 51
Time to head back and review the property Return to the
property
Slide 52
Return to The Properties
Slide 53
Question #8: (x 2 y 3 ) 4 = ? x6y7x6y7 xy 9 x 8 y 12
Slide 54
Be careful, you are using more than one property at a time here
Return to the problem
Slide 55
Return to The Properties
Slide 56
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 57
Be careful, you are using more than one property at a time here
Return to the problem
Slide 58
Return to The Properties
Slide 59
Question #10: = ?
Slide 60
Be careful, you are using more than one property at a time here
Return to the problem
Slide 61
Congratulations! You really know your exponent properties! Show
Mr. Preiss this screen so can award you full credit for completing
this activity.