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How do you Solve the equation w equals Cr to the negative second power for r?
Wiki User
∙ 13y ago
Assuming the equation described is: w = (Cr)-2...
Remember that any value to a negative power can also be represented like this:
(Cr)-2 = 1/(Cr)2
Also note that we can distribute the power over multiplication. (This doesn't apply to addition!)
(Cr)2 = C2r2
So if we rewrite the equation with this, we get
w = 1/(C2r2)
If we invert both sides and then divide by C2 on both sides, we get
1/w = C2r2 → 1/(wC2) = r2
Take the square root of both sides, and you'll have the equation in terms of r:
r = sqrt[1/(wC2)]
The biggest step was realizing that anything to a negative power can be inverted to find the same with a positive power. For example, 2-2, if you type it in your calculator, gives you 0.25, or 1/4. If we do what we did above, we can take 2-2 and make it 1/(22), which also equals 1/4. This applies to any negative power, and is a powerful technique for solving equations with negative exponents.
Wiki User
∙ 13y ago
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