Solve 2^-3-32^-4/2^-3

$$\frac { 2 ^ { - 3 } - 32 ^ { - 4 } } { 2 ^ { - 3 } }$$

Evaluate

$$\frac{131071}{131072}\approx 0.999992371$$

Solution Steps

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

$$\frac{\frac{1}{8}-32^{-4}}{2^{-3}}$$

Calculate 32 to the power of -4 and get \frac{1}{1048576}.

$$\frac{\frac{1}{8}-\frac{1}{1048576}}{2^{-3}}$$

Subtract \frac{1}{1048576} from \frac{1}{8} to get \frac{131071}{1048576}.

$$\frac{\frac{131071}{1048576}}{2^{-3}}$$

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

$$\frac{\frac{131071}{1048576}}{\frac{1}{8}}$$

Divide \frac{131071}{1048576} by \frac{1}{8} by multiplying \frac{131071}{1048576} by the reciprocal of \frac{1}{8}.

$$\frac{131071}{1048576}\times 8$$

Multiply \frac{131071}{1048576} and 8 to get \frac{131071}{131072}.

$$\frac{131071}{131072}$$

Factor

$$\frac{131071}{2 ^ {17}} = 0.9999923706054688$$