Simplify $\dfrac{16 \cdot 2^{n+1} - 4 \cdot 2^{n}}{16 \cdot 2^{n+2} - 2 \cdot 2^{n+2}}$.

Question

Aicharya · Accepted Answer

Numerator: $2^{n}(16 \cdot 2 - 4) = 2^{n}(32 - 4) = 28 \cdot 2^{n}$. Denominator: $2^{n+2}(16 - 2) = 4 \cdot 2^{n} \cdot 14 = 56 \cdot 2^{n}$. Ratio $= \dfrac{28}{56} = \dfrac{1}{2}$.

Simplify $\dfrac{16 \cdot 2^{n+1} - 4 \cdot 2^{n}}{16 \cdot 2^{n+2} - 2 \cdot 2^{n+2}}$.

Solution