SOLUTION: w=cr^(-2) solve for r

Question 403368: w=cr^(-2) solve for r
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

"Solve for r" means we want r by itself on one side of the equation. So we want to "remove" the c in front and the exponent of -2. First we will divide by c which, as you will see, will "move" the c over to the other side of the equation:

Now we have an equation that tells us what is. We want an equation that tells us what "r" is. The exponent on "r" is a 1. (Any "invisible" exponent is always a 1.) So we want to find a way to change the exponent from a -2 into a 1. To do this we will combine several ideas:

It is OK to raise both sides of an equation to the same power.
The rule for exponents when raising a power to a power is to multiply the exponents.
Multiplying reciprocals always results in a 1!

So if we raise both sides of the equation to the reciprocal of -2 power, the exponent on r will turn into a 1! The reciprocal of -2 is -1/2. So we will raise both sides of the equation to the -1/2 power:

On the right side we get or just r, exactly as we planned:

This may be an acceptable form for the answer. Or we could do some things on the left side:

This may be the preferred form for the answer.
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