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How To Solve Negative Exponents ( PreAlgebra)
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Feb 19, 2025
In today’s lesson , we will work with negative exponents , a lot of students tend to be allergic to them but they are not that complicated once you understand the key concept to working with them
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0:01
so last week we discussed exponent and
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we talked about a key concept so that's
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why I'm recording it this morning
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basically x 5 over x 3 is = x 5 - three
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so what you do is just you div you when
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you're dividing exponents or Expressions
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that have exponent with the same base
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you're subtracting them and the way you
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subtract them is this according to the
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formula below so
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if you have a to the power B over a^ C
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this is equal to
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a^ B- C and this is what we doing here
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okay so x 5 over X 3r is x 5 - 3 which
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gives you X to 2 or x² so now basically
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this is again a formula that we
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recalling from last week all right but
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the base I have to be the same if the
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base is not the same you cannot do that
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so they have to have the same base when
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I say base I mean here the base is two
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the base is two the exponent is six and
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the exponent here is three so they have
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to have the same base if the base is not
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the same you cannot use this formula all
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right so again make sure uh the
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expression of the monomial has the same
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base now here now we have a little bit
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of a problem right so I put water about
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so if I have x 3r / x 5 I put X and a
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question mark so the question mark is
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how do you solve this again we're going
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to use the same principle we're going to
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use the a the B over a the C principle
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right so we have B minus C so this gives
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you pretty much x 3 - 5 now if you know
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your uh arithmetic 3 - 5 is = to x -2
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right so this is x -2 that we have here
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the same process here right 2 3r over 2
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6 is 2 3 - 6 which is basically 2 to the
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-3 now what we have is we have an
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introduction of A New Concept and this
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is called a negative exponent this is a
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negative exponent because the exponent
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is no longer a positive number but is a
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negative number now the problem is this
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in mathematics we never want to leave
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negative exponent the same way they are
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we have to turn them into positive
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exponents so how do we do that again
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there a key concept so x n is equal to
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1/ X N so this is how you go from a
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negative exponent to a positive exponent
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so how would you change this according
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to this formula because this is x
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-2 it becomes
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1/ x 2 so this a really really really
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simple uh concept to use okay again you
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never want to leave negative exponent
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this is just a rule that we have in
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mathematics you never want to leave
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negative exponent you always want to
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turn them into positive exponent now how
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do you deal with a numb this is 2 the -3
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so that gives you 1 over 2 cubed and 2
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Cub you all know is 8 so this is 1 over
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8 okay and I give you another example
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here 3 to the2 is 1/ 3 S now if you feel
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like doing some more work I give you a
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bunch of examples here that you can work
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on all right so we know you want to
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write each expression using the positive
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exponent so 2 5 will be what 1/ 2 5 and
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4 -3 will be 1 over 4 3r 5 -2 is 1 5 2
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6-1 is 1 6 and then x -7 1 x 7 y -10 1 y
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10 and then 2 x 3 now change it up a
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little bit 2x3 now you have to be
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extremely careful here right because the
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2 is not ra to the power of3 two is just
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two so now this becomes what two times
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now we're going to turn this into a
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positive exponent 2 * 1/ x to the 3r now
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the two is not the denominator so now A
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good rule of thumb is this when I tell
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my student all the time when you have
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this you don't want to get confused make
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sure you write two over one so that way
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you know to multiply you go across right
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so that gives you 2 over X cubed okay so
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2 X3 will give you 2 over X Cub again
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this is simple negative exponent I'm not
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that complicated people get scared but
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if you understand the simple principle
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you can work on it all right so again
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the key concept is this one here all
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right so I hope this helped you guys out
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any questions feel free to send me a
4:57
message thank you and have a good day