all right ladies and gentlemen I want to
let you know on a secret I originally
wanted to title this video three stupid
mistakes students make but I didn't want
to put stupid in the title but they
really are stupid mistakes and the only
reason why I feel comfortable saying
stupid mistakes is because they are
mistakes that I have made probably even
on some YouTube videos or in front of my
students but I didn't want to put it on
a YouTube title people sometimes get
argumentative about that so we're going
to keep with three simple mistakes but
now that you're watching the video you
know what I originally wanted to call it
so what are some mistakes that students
make when they're doing rules of
exponents and these are basic problems
of rules of exponents but students like
myself still make mistakes what is the
most common one here students multiply
they see that the multiplication problem
they say oh yeah I got to multiply these
so that's going to be X to 5 * 7 which
equals x to the 35th power no ladies and
gentlemen that is not correct remember
the rules of exponents say the product
property when you're multiplying two
exponents with the same base you're
going to add the powers this is going to
be x to the 12th power okay make sure
you're clear on that the next one
students are like oh yeah multiply
product property you multiply you add so
when you divide you subtract right I get
it so they say all right that's 5 to the
5 - 8 that's y to the -3 crap what do I
do with the -3 hm usually students will
just make something up and say I just
want to forget about theg -3 and they'll
just leave the three in the top no
ladies and gentlemen remember when you
have a negative power to only way to get
rid of that negative power is to
reciprocate that means you need to be
able to put this in the denominator so
therefore this is going to be 1 over a y
to the pos3 this happens all the time
students get to this answer and they're
like yeah that's it that's what we do
but then they flip it or they just kind
of get rid of the negative like uh I
didn't see it don't do that the next one
negatives they mess students up all the
time right now we talked about over here
where will students will get the
negative and they will kind of forget to
reciprocate but what if you already have
a fraction how do you already
reciprocate that and what if you have a
negative inside there so there's a
couple mistakes actually students will
make here the first mistake is that
they'll see like negatives will cancel
out I don't know they think we're doing
multiplication here so they'll say oh
well this is just going to be a 1/ now
squared and therefore it's a 1 over 25
cuz maybe the negatives cancel out no
that's not the rule that doesn't work
that way the other way is sometimes
students will just kind of get confused
on how do we reciprocate this and maybe
they will just they'll forget about the
negative they'll leave it as a negative
inside there they'll forget that this is
a negative number squared but one quick
way to always do this remember you just
got to reciprocate this number just like
we did with the Y we change it to Y you
know 1 over Y3 which is the same thing
as 1 over y to the thir power it's the
same idea so all we simply need to do is
just reciprocate this so therefore it's
going to be5 over 1 to the positive
second power once you reciprocate you
can now change that to a positive power
now again we don't really need to go
ahead and include this here but a lot of
students again will forget about the
negative and they'll leave that as a -25
no no no this is5 * 5 so therefore the
final answer is going to be a positive
25
