1. $\displaystyle a^{-\frac{m}{n}} = \frac{1}{a^{m/n}} = a^{n/m}$

$\displaystyle 2x^{-1/2} = \frac{2}{x^{1/2}} = \frac{2}{\sqrt{x}}$

I'm not sure where the 2 on the denominator comes from

$\displaystyle \frac{2}{\sqrt{x}} = 8 then \frac{1}{\sqrt{x}} = 4$

Take the reciprocal of both sides

$\displaystyle \sqrt{x} = \frac{1}{4}$

$\displaystyle x = \frac{1}{16}$

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2. Use the log power law:

$\displaystyle a\, \log _b(c) = \log _b (c^a)$

$\displaystyle 3\log_{10}(6) = \log_{10} (6^3) = \log_{10} (216)$