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# Order of operations examples: exponents

Video transcript

So I have six
different expressions here, and what I want you
to do is pause this video and try to calculate the value
of each of these expressions. I'm assuming you've
given a go at it. Now let's work through them. So when we see
something like this, we have to remember our
order of operations. We have 2 times
3 squared, and we have to remember that the
first thing we would need to think about are
the parentheses. I'll just write paren for short. Then we worry about exponents. Then we will worry about
multiplication and division, and actually let me
write it this way. We worry about
multiplication and division. And then we worry about
addition and subtraction. So in this expression
right over here, there are no parentheses, so
we do the exponents first. So we calculate
what 3 squared is. 3 times 3 is 9, so
this becomes 2 times 9, which is equal to 18. Now let's look at this one,
and this one is interesting, because they have-- it looks
like the same expression, but now there are parentheses. And because of
these parentheses, we're going to do
the multiplication before we take the exponent. So 2 times 3 is going
to be 6, and we're going to take that
to the second power. So that's 6 times 6,
which is equal to 36. Now let's think about
this one right over here. Once again, we want to do our
multiplication and our division first. So we have a division
right over here. 81/9 is the same thing
as 81 divided by 9, and that's going to be 9. And then we have-- so it
becomes 1 plus 5 times 9. Now we want to do the
multiplication before we do the addition, so
we're going to do our 5 times 9, which is 45. So this becomes 1 plus 45,
which of course is equal to 46. Now let's tackle this
one right over here. So, we would want to
do the exponents first. So, 1 squared, well
that's just going-- let me do this in
a different color. 1 squared is just
going to be equal to 1, so that's just going
to be equal to 1. And so you have
2 times 4 plus 1. What should you do? Should you add first or do
the multiplication first? Well multiplication takes
precedence over addition, so you're going to do
the 2 times 4 first. 2 times 4 is 8, so
you're going to have 8 plus 1, which of
course is equal to 9. Now you have a very
similar expression, but you have parentheses. So that's going to force you
to do what's in the parentheses before you take the exponent. But within the parentheses
we have multiplication and addition, and
we have to remember that we do the
multiplication first. So we're going to
do the 2 times 4 first, so that's going to be
8 plus 1 to the second power. 8 plus 1 is 9, so that's
9 to the second power. 9 squared is the same thing as
9 times 9, which is equal to 81. Now we have one
more right over here that looks very
similar to this one, except, once again, we
have parentheses that's making us do the addition first. Without parentheses, we
would do the multiplication and the division first. But here, we see
that 1 plus 5 is 6, and then we have this
81/9, which is 9. So this simplifies to 6 times 9,
which of course is equal to 54.