<s>[INST] Solving for $x$ in $y=N\cdot\left(\frac{10}{x}\right)^{-2.6}$ I want to confirm my solution of $x$ from 
$$y=N\cdot\left(\frac{10}{x}\right)^{-2.6}$$ 
My answer is:
$$x=\frac{N^{2.6}}{10\cdot y^{2.6}}$$ 
Is this right? How would you solve? 
 [/INST] Let $$y = N \cdot (\frac{10}{x})^{-2.6}$$
Then,
$$y \cdot (\frac{10}{x})^{2.6} = N$$
$$ y \cdot 10 ^{2.6} = N \cdot x^{2.6}$$
$$ (y \cdot 10^{2.6})^{1/2.6} = (N \cdot x^{2.6})^{1/2.6}$$
$$ y^{1/2.6} \cdot 10 = N^{1/2.6} \cdot x$$
$$ x = y^{1/2.6} \cdot 10 \cdot N^{-1/2.6} = (\frac{y}{N})^{1/2.6} \cdot 10 $$
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