If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

Current time:0:00Total duration:2:39

- [Instructor] Which of
the following is equivalent to all of this stuff right over here. One over 88, or 1/88,
y to the 100 plus one, minus this entire expression, 1/44 y to the 100 minus 1/2. So let me just rewrite it. So this part right over here, this is going to just be one over 88 y, let me make sure it looks clear, y to the 100th power plus one, and then we're gonna subtract all of this. So one way to think about
it is we could distribute this negative sign, so it's gonna be, it's going to be negative, one way you could think
about it is negative one, negative one times all of this business. So it's gonna be minus one
over 44 y to the 100th, and then a negative, remember,
we're gonna distribute it, so negative one times negative 1/2 is going to be plus, plus 1/2. Now, let's see what we can
do to further simplify it. So this is 1/88 y to the 100. This is minus, or you could say negative, 1/44 y to the 100th. And so we can add these
two terms together. This is going to be, we could write this, one over 88 minus one over 44 y to the 100th, and then you have plus one, plus 1/2, so that's pretty straightforward. So you have plus one, plus 1/2, so that's gonna be plus 3/2, plus 3/2. And now we just have to
figure out what this is. So 1/88 minus 1/44, well,
the common denominator here could be 88. That is the least common
multiple of 44 and 88. 88 is divisible by 44. So if we multiply the
denominator by two, you get 88. You multiply the numerator
by two, you get two. 2/88 is the same thing as 1/44. So this 1/88 minus 2/88. Well, this is going to give
us, this right over here is going to give us, if we, this is going to give us
minus, or negative, 1/88. 1/88 minus 2/88 is going
to be negative 1/88, y to the 100, y to the 100, plus 3/2, plus 3/2. And that is negative
1/88th y to the 100th, y to the 100th plus 3/2. This choice right over here.