Solve 2^-2+2^-3/2^-5+2^-7

$$\frac { 2 ^ { - 2 } + 2 ^ { - 3 } } { 2 ^ { - 5 } + 2 ^ { - 7 } }$$

Evaluate

$$\frac{48}{5}=9.6$$

Solution Steps

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

$$\frac{\frac{1}{4}+2^{-3}}{2^{-5}+2^{-7}}$$

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

$$\frac{\frac{1}{4}+\frac{1}{8}}{2^{-5}+2^{-7}}$$

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

$$\frac{\frac{3}{8}}{2^{-5}+2^{-7}}$$

Calculate 2 to the power of -5 and get \frac{1}{32}.

$$\frac{\frac{3}{8}}{\frac{1}{32}+2^{-7}}$$

Calculate 2 to the power of -7 and get \frac{1}{128}.

$$\frac{\frac{3}{8}}{\frac{1}{32}+\frac{1}{128}}$$

Add \frac{1}{32} and \frac{1}{128} to get \frac{5}{128}.

$$\frac{\frac{3}{8}}{\frac{5}{128}}$$

Divide \frac{3}{8} by \frac{5}{128} by multiplying \frac{3}{8} by the reciprocal of \frac{5}{128}.

$$\frac{3}{8}\times \frac{128}{5}$$

Multiply \frac{3}{8} and \frac{128}{5} to get \frac{48}{5}.

$$\frac{48}{5}$$

Factor

$$\frac{2 ^ {4} \cdot 3}{5} = 9\frac{3}{5} = 9.6$$