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jmc

algebra senior

Problem

Simplify:

\frac{2 ^{n + 4} - 2 ( 2 ^{n} )}{2 ( 2 ^{n + 3} )}

. Express your answer as a common fraction.

Solution

Note that

\frac{2 ^{n + 4} - 2 ( 2 ^{n} )}{2 ( 2 ^{n + 3} )} = \frac{2 ^{n}}{2 ^{n}} \cdot \frac{2 ^{4} - 2}{2 ( 2 ^{3} )} = \frac{7}{8}

.

Final answer

\frac{7}{8}