Why does $3^{16} \times 7^{-6}$ become $\frac{3^{16}} {7^{6}}$? I was doing an exercise on exponents:
$$\begin{align}
\left(3^{-8} \times 7^3\right)^{-2} &= \left(3^{-8}\right)^{-2}\times \left(7^3\right)^{-2} \\ 
&= 3^{16} \times 7^{-6} \\
&= \frac{3^{16}} {7^{6}} \\
\end{align}$$
Why did $7^{-6}$ turn to $7^{6}$? More generally, why does a negative exponent turn positive when moved to the denominator?  Would appreciate kindergarten language ;-D

$$ 7^{-6}= 7^{6*-1} = {(7^6)}^{-1}$$ and $${x}^{-1}=\frac{1}{x}$$ so $$ 7^{-6}= {(7^6)}^{-1}=\frac{1}{{7}^{6}}$$ the first and second equation could be proven using the laws of exponents.
