Solve (4^0+4^-1)div(4^0-4^-1)

$$( 4 ^ { 0 } + 4 ^ { - 1 } ) \div ( 4 ^ { 0 } - 4 ^ { - 1 } )$$

Evaluate

$$\frac{5}{3}\approx 1.666666667$$

Solution Steps

Calculate 4 to the power of 0 and get 1.

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

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

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

Add 1 and \frac{1}{4} to get \frac{5}{4}.

$$\frac{\frac{5}{4}}{4^{0}-4^{-1}}$$

Calculate 4 to the power of 0 and get 1.

$$\frac{\frac{5}{4}}{1-4^{-1}}$$

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

$$\frac{\frac{5}{4}}{1-\frac{1}{4}}$$

Subtract \frac{1}{4} from 1 to get \frac{3}{4}.

$$\frac{\frac{5}{4}}{\frac{3}{4}}$$

Divide \frac{5}{4} by \frac{3}{4} by multiplying \frac{5}{4} by the reciprocal of \frac{3}{4}.

$$\frac{5}{4}\times \frac{4}{3}$$

Multiply \frac{5}{4} and \frac{4}{3} to get \frac{5}{3}.

$$\frac{5}{3}$$

Factor

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$