WEBVTT
Kind: captions
Language: en
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ok this module is about rules of
exponents so what is X to power mean? it means
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you take X multiplied it by itself a
times for example X to the fifth is x
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x x x x five times what if i want to
find the x to the a times X to the
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b remember X to the a means i take x x
x multiplied it up a times and then this
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is going to be x to the b
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the practical effect is just a long
string of X is how many x's do i have a
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of them and have b of them i'm
going to have x 8 plus B of them that
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tells me that X to the a times x to
the B is next to the a plus B that's our
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first rule for example x to the third
times x 4 x 3 plus 4 which is x to
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the 7 notice it's not three times four
so remember X cubed is X to the third
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the same as X cubed and x to the fourth is x
4 x so just roll it out that would be
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x x x x x x x, 7 times whish is x to the 7
okay second rule what about x to the a divided by x to the b. well now i have x times x
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times x a time, divided by x times x times x b times
so i'm dividing i'm going to cancel all
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those X's and i'm just going to be left
over so what's gonna be left over is a
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minus B x to the a over X to b so xto the a minus b so if i have x to the 8/ x to the 3 thats
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x to the 8-x to the 3 which is X to the fifth and we
can convince ourselves that's true
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because x to the 8, 8 x's on top
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to the three is three x's on the bottom
those cancel and you're left with 5 x's
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now you may say what happened that more x's on the bottom then on the top well this is gonna come out a
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negative number so what does that mean
to have a negative number
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well that would be 1 over so let's just
do an example suppose i had X to the 3 over x to the 5 X to the
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negative 2 so what does that look like y
x times X times X on top
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x times X times X times X on the bottom 3 x's
cancel left with 1 over s square so X to
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the minus 2 must be one over X to he poritive 2 this is another rule
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that says x to the negative a is 1 over X
to the positive a next rule, what if i have x to the positive a
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raised to the a thats x to the a times X to the a
times X to the a x to the a B times so
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I'm going to have X to the a/b time so
remember this is X to the a+ a+ a+ a B
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times X to the a times B for example X
square cube that's going to be best to
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thats gonna be x to the 2 times 3
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which is x to the 6 because that x squared
cubed is x squared times x squared times x
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squared which is X to the two plus two
plus two notices thats 3 of them which is X to the
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six ok let's go back to the division for
a second
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what if the power of the top of the
bottom is the same
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what if have X to the a divided a to the a that would be X to the a minus a which ould
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be x to the 0 since the x's are the same
that's just come out 1 so X to the 0 is
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always one so say i had x cubed on top and x cubed on the bottom, which is x to the 0 which is 1
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been wondering y 0 power is one it
means the power on top of the power on
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the bottom are the same so let's make a
list of the rules we've learned so far
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we learned that X to the a times X B is
X to be a plus B and X to the a divided
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by x to the b is x to the a minus b, where x to the b is x to the a times b and x to the minus a
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or x to the positive a and we learned that x to the 0 is positive 1
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ok suppose I want to find
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I knew that X how do i want to show a
root was like know that X cubed equals
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a so I say to myself for what power x is
x alone is what power a well i have
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to take something and multiplied it by
itself three times a that gives me a thats each of
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these individually must be the cubed root of a
because the cubed root of a times the
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cube root of a times the cube root of a
equals a so that means that this would
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be what power
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well the third power because if i take a
to the 1/3 times a to the 1/3 times
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a to the one-third and you get one-third
plus one-third plus one-third which is
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one which is a to the one so in general if i want
to find X to the 1 over a thats a root
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of x many people confuse the negative
power with the root power as a reminder x to the
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negative 2 is one over x
square X to the one-half is the square
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root of x so don't confuse the fact that
this is a fraction with this fraction