Rewrite Using Positive Exponents


Uploaded by mwelmes on 29.06.2009

Transcript:
REWRITE THE EXPRESSION USING ONLY POSITIVE EXPONENTS.
For the following problem, I'd like to rewrite the expression
using only positive exponents.
So our first expression we have,
2x^-5
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
1/2^3
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
y^3/8
Because 2*2*2 is 8.
So you can see, these two answers match.
That completes our lesson on negative exponents.