Solve frac{2^{0}+2^-1+2}{2^-2+2^-3+2^-4}

$$\frac { 2 ^ { 0 } + 2 ^ { - 1 } + 2 } { 2 ^ { - 2 } + 2 ^ { - 3 } + 2 ^ { - 4 } }$$

Evaluate

$$8$$

Solution Steps

Calculate 2 to the power of 0 and get 1.

$$\frac{1+2^{-1}+2}{2^{-2}+2^{-3}+2^{-4}}$$

Calculate 2 to the power of -1 and get \frac{1}{2}.

$$\frac{1+\frac{1}{2}+2}{2^{-2}+2^{-3}+2^{-4}}$$

Add 1 and \frac{1}{2} to get \frac{3}{2}.

$$\frac{\frac{3}{2}+2}{2^{-2}+2^{-3}+2^{-4}}$$

Add \frac{3}{2} and 2 to get \frac{7}{2}.

$$\frac{\frac{7}{2}}{2^{-2}+2^{-3}+2^{-4}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{\frac{7}{2}}{\frac{1}{4}+2^{-3}+2^{-4}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{\frac{7}{2}}{\frac{1}{4}+\frac{1}{8}+2^{-4}}$$

Add \frac{1}{4} and \frac{1}{8} to get \frac{3}{8}.

$$\frac{\frac{7}{2}}{\frac{3}{8}+2^{-4}}$$

Calculate 2 to the power of -4 and get \frac{1}{16}.

$$\frac{\frac{7}{2}}{\frac{3}{8}+\frac{1}{16}}$$

Add \frac{3}{8} and \frac{1}{16} to get \frac{7}{16}.

$$\frac{\frac{7}{2}}{\frac{7}{16}}$$

Divide \frac{7}{2} by \frac{7}{16} by multiplying \frac{7}{2} by the reciprocal of \frac{7}{16}.

$$\frac{7}{2}\times \frac{16}{7}$$

Multiply \frac{7}{2} and \frac{16}{7} to get 8.

$$8$$

Factor

$$2^{3}$$