<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] First, notice that
$$
y = N \cdot \left( \dfrac{10}{x} \right)^{-2.6} = N \cdot \left( \dfrac{x}{10} \right)^{2.6}
$$
Next, divide both sides by $N$:
$$
\dfrac{y}{N} = \left( \dfrac{x}{10} \right)^{2.6}
$$
Now exponentiate with $\frac{1}{2.6}$ to get
$$
\left( \dfrac{y}{N} \right)^{\frac{1}{2.6}} = \dfrac{x}{10}
$$
Finally, multiply by $10$:
$$
10 \cdot \left( \dfrac{y}{N} \right)^{\frac{1}{2.6}} = x
$$
</s>