CEMC Pascal

Algebra Difficulty 1.8 Junior Find the answer

The value of $\frac{2^4 - 2}{2^3 - 1}$ is?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

We note that $2^3 = 2 \times 2 \times 2 = 8$ and $2^4 = 2^3 \times 2 = 16$ . Therefore, $\frac{2^4 - 2}{2^3 - 1} = \frac{16 - 2}{8 - 1} = \frac{14}{7} = 2$ . Alternatively, $\frac{2^4 - 2}{2^3 - 1} = \frac{2(2^3 - 1)}{2^3 - 1} = 2$ .

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