Solve 4^-5-4^-2/4^-3+4^-4

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

Evaluate

$$-\frac{63}{20}=-3.15$$

Solution Steps

Calculate 4 to the power of -5 and get \frac{1}{1024}.

$$\frac{\frac{1}{1024}-4^{-2}}{4^{-3}+4^{-4}}$$

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

$$\frac{\frac{1}{1024}-\frac{1}{16}}{4^{-3}+4^{-4}}$$

Subtract \frac{1}{16} from \frac{1}{1024} to get -\frac{63}{1024}.

$$\frac{-\frac{63}{1024}}{4^{-3}+4^{-4}}$$

Calculate 4 to the power of -3 and get \frac{1}{64}.

$$\frac{-\frac{63}{1024}}{\frac{1}{64}+4^{-4}}$$

Calculate 4 to the power of -4 and get \frac{1}{256}.

$$\frac{-\frac{63}{1024}}{\frac{1}{64}+\frac{1}{256}}$$

Add \frac{1}{64} and \frac{1}{256} to get \frac{5}{256}.

$$\frac{-\frac{63}{1024}}{\frac{5}{256}}$$

Divide -\frac{63}{1024} by \frac{5}{256} by multiplying -\frac{63}{1024} by the reciprocal of \frac{5}{256}.

$$-\frac{63}{1024}\times \frac{256}{5}$$

Multiply -\frac{63}{1024} and \frac{256}{5} to get -\frac{63}{20}.

$$-\frac{63}{20}$$

Factor

$$-\frac{63}{20} = -3\frac{3}{20} = -3.15$$