Simplify using properties of exponents


In this video I’d like to simplify
the following expressions using properties of exponents.
So for the first expression, well sometimes I’d like to actually
break this up a little bit. Right, I’m going to draw a little circle
around the negative 9 and the 3. Negative 9 divided by positive 3,
well that’s easy to see. That’s just negative three.
Now the properties of exponents say when I have division
with the same base, our base is x,
I can subtract the exponents. So this becomes x,
we write our base, and we subtract the exponents
from top to bottom. So we have eight thirds
minus two thirds which you can see
becomes 6 over 3. Now the 6 over 3
can be reduced to become 2. So our final answer
is negative 3 x squared. For the second problem, well
I’d like to distribute our exponent so we’re going to rewrite this
as negative 2 raised to the second, the next piece
is x to the one third, that’s going to become
x to the two over three. Where did the two thirds come from?
2 times one third is two thirds and the last piece is y
to the 2 over 4. Again 2 times one fourth
is two fourths. Now we can clean this up
a little bit. Negative 2 squared
is positive 4, right? Because we have negative 2
times negative 2. X to the two thirds, well there’s
nothing we’re going to do with that, that’s just going to stay
x to the two thirds and the last piece,
y to the two fourths, well that’s going to be reduced
to y to the one half. And there’s our final answer.

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