Download - exponents
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Exponents
VINCENT LEPING
08/03/2014
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For Learning to Happen!
•Clear your desk of anything that may distract you.
•Remove all other thoughts from your mind.
•Pay close attention.•Try all the examples.•Ignore all other distractions.
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Definition of Exponent
An exponent tells how many times a number is multiplied by itself.
3 4Base
Exponent
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Review:
What do exponents tell us?
What does 53 mean?
53 =5 5 5
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What is the “base”?What is the “exponent”?
8 5BaseExponent
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What an Exponent Represents
An exponent tells how many times a number is multiplied by itself.
34= 3 x 3 x 3 x 3
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Write 63 in standard form.
63 = 6 6 6 = 216
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Write 64 in standard form.64 = 6 6 6 6
= 1,296
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What happens if we multiply 63 64?63 64=(6 6 6) (6 6 6 6)
63 64
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So…63 64= 67 because we used 6 as a factor seven times!
Notice anything?
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Let’s try another example:
What is 52 54?
52 54 = (5 5) (5 5 5 5)
or 52 54 = 56
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For MULTIPLICATION:
x s x t = x s + t
(For any number x and for integers s and t.)
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In other words, when multiplying two numbers in exponential form with the same base, add the exponents.
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Ex:9 4 9 8 = ?
9 12
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What happens if we divide?75
73
75 = 7 7 7 7 7
73 7 7 7
Cancel out any numbers that are in the numerator AND denominator!
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After we cancel, we are left with 72.
So, 75 = 72
73
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For DIVISION:
xs =
xt
(For any nonzero number x and for integers s and t.)
x s - t
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In other words, when dividing two numbers in exponential form with the same base, subtract the exponents.
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Ex:6 8 ÷ 6 5 = ?
6 3
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What about (52)3?(52)3
(52) (52) (52)
(5 5)(5 5)(5 5)
56
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Raising a power to a power:
(xs)t = x s t
(For any number x and for integers s and t.)
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In other words, when raising a number with an exponent to a power, multiply the exponents.
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Ex:(5 3) 7 = ?
521
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One important thing to remember…x0 = 1
(Any number to the zero power is equal to 1!)
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Why???For example…
32 ÷ 32 = 3 2 - 2 = 30
32 = 3 3 = 9 = 1
32 3 3 9
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So, 30 = 1This works for any base number!
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Can we have negative exponents?
Yes! Negative exponents represent the reciprocal.
The reciprocal of x is
The reciprocal of 10 is
They do NOT make the answer negative.
x
1
10
1
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5 -2 = =
2-4=
25
1
25
1
16
1
2
14
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REFERENCE LIST
Melnichenko, Y. (2008, September 14). Exponents. Retrieved March 08, 2014, from http://www.slideshare.net/yelena585/exponents-presentation
Yuskaitis, M. (2008, June 06). Exponents. Retrieved March 08, 2014, from http://www.slideshare.net/hiratufail/exponents1