The question is this:
$$\frac{1}{R^p} = \frac{1}{4.5\times 10^2} + \frac{1}{9.4\times 10^2}$$
I calculated the equation so that it simplifyed to:
$$\frac{1}{R^p} = 0.003286$$
But now I am stuck...
Thanks for any help!!
$\endgroup$ 13 Answers
$\begingroup$I will assume you are asking how to manipulate the equation to get the variable out of the denominator (the numerator is the "top" of the fraction, and the denominator is the bottom of the fraction):
Cross multiply, and then divide $$\frac{1}{R^p} = 0.003286 \iff 1= 0.003286\cdot R^p \iff R^p = \frac 1{0.003286}\approx 304.3$$
$\endgroup$ 3 $\begingroup$Let us assume $R\neq 0$; you can multiply both sides by $R^p$:
$$R^p\frac{1}{R^p}=R^p 0.003286,$$
i.e.
$$1= R^p 0.003286.$$
Now, dividing both sides by $0.003286\neq 0$ you are arrive at
$$ R^p=\frac{1}{ 0.003286}.$$
$\endgroup$ $\begingroup$You can reciprocate both sides of the equation. That is: $$\frac{1}{a} = b \implies a = \frac{1}{b}$$
(assuming $b\ne 0$)
So, in your case:
$$\frac{1}{R^p} \approx 0.003286 \implies R^p\approx \frac{1}{0.003286}\approx304.3$$
EDIT:
Another approach that is sometimes helpful depending on what $p$ is equal to:
$$\frac{1}{a^b} = a^{-b}$$
So, in your case: $$\frac{1}{R^p} = R^{-p}\approx 0.003286\implies R \approx 0.003286^{-1/p}$$
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