Rewrite Using Positive Exponents

Uploaded by mwelmes on 29.06.2009

For the following problem, I'd like to rewrite the expression
using only positive exponents.
So our first expression we have,
So really, the two is by itself and we have an x^-5.
We're multiplying 2 times x^-5.
So again, the 2 stays where it is.
And to take care of this negative exponent we take the reciprocal of the base.
Our base in this case is x.
So the reciprocal of x is 1/x.
Now we take the exponent and make it positive.
So x^-5 is really the same as 1/(x^5).
And when we clean this up we have
2*1 is 2, over x^5.
And that's our final answer.
Next we have (2/y)^-3.
I'm actually going to do this problem two separate ways.
The first way, and usually the way I prefer,
would be to take the reciprocal of the base.
In this case our base is 2/y.
So I can rewrite that as (y/2)^3.
So what did I do?
I took the reciprocal of my base, and made the exponent positive.
And that's my final answer.
Well, actually, I can clean this up a little bit further.
I can go y cubed over 2 cubed (y^3/2^3).
And then I'm left y^3 over 8.
Because 2*2*2 is 8.
Last problem.
So we're going to do this another way
and hopefully we end up with the same answer.
I can actually say 2^-3/y^-3.
So now, 2^-3, well my base is 2.
So if I take the reciprocal of that, I'm left with
Times the reciprocal of 1/y is y/1.
And I make the exponent positive.
Now I'm left with 1*y^3 = y^3
2^3*1 is 2^3
And then when we finish our problem we're left with
Because 2*2*2 is 8.
So you can see, these two answers match.
That completes our lesson on negative exponents.