<s>[INST] How to simplify this indices question The question:

$$ \mbox{(d)} \ \ \frac{ \frac{ 4^{ n + 1 } }{ 2^{ -n } } - 8^n }{ 2^{ 3n + 2 } } $$

And here are my workings:
$$   2. \quad
     \frac{ \frac{ 4^{ n + 1 } }{ 2^{ -n } } - 8^n }{ 2^{ 3n + 2 } }
   = \frac{ 2^{ 2n + 2 } \div 2^{ -n } - 2^{ 3n } }{ 2^{ 3n + 2 } }
   = \frac{ 2^{ 2n -(-n) + 2 } - 2^{ 3n } }{ 2^{ 3n + 2 } }
   = \frac{ 2^{ 3n + 2 } - 2^{ 3n } }{ 2^{ 3n + 2 } }
\\ = \frac{ 2^{ 3n } \times 2^2 - 2^{ 3n } }{ 2^{ 3n } \times 2^2 }
   = \frac{ 4 \times 2^{ 3n } - 2^{ 3n } }{ 4 \times 2^{ 3n } }
$$
I am unable to proceed to the next step can someone please help? Or did i did something incorrect? Btw from the left to right
 [/INST] You have $\displaystyle \frac{4 \cdot 2^{3n} - 2^{3n}}{4 \cdot 2^{3n}}=\displaystyle \frac{3 \cdot 2^{3n}}{4 \cdot 2^{3n}}$
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