$$2^{10 - x} \cdot 2^{10 - x} = 4^{10-x}$$ Is that correct?
I would've done
$$ 2^{10 - x} \cdot 2^{10 - x}\;\; = \;\; (2)^{10 - x + 10 - x} \; = \; (2)^{2 \cdot (10 - x)} \;=\; 4^{10 - x}\tag{1} $$
Is that allowed?
If so, can I say that
$$ \frac{4^x}{2^y} = 2^{x - y} \tag{2} $$