<s>[INST] Express the following in terms of y. If $y = 2^{2x}$, express the following in terms of y.
$2^{2x-1} - 4^{2x+1} + 16^{x-1}$
I began it in this way:
$2^{2x}\cdot 2^{-1} - (2^2)^{2x+1} + (2^4)^{x-1}$
$2^{2x}\cdot \frac{1}{2} - 2^{4x}\cdot2^2 + 2^{4x}\cdot2^{-1}$
$2^{2x}\cdot\frac{1}{2}-2^{2x}\cdot2^{2x}\cdot2^2+2^{2x}\cdot2^{2x}\cdot\frac{1}{2}$
$\frac{y}{2} - 4y^2 + \frac{y^2}{2}$
Is this right?
 [/INST] Almost. Note that $$(2^4)^{x-1}=2^{4(x-1)}=2^{4x-4}=2^{4x}\cdot2^{-4}\ne2^{4x}\cdot 2^{-1}.$$ Also note that you can gather like terms (specifically, the $y^2$ terms).
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