Solve {left(0.155/0.60-1/2500right)}^-1

$${ \left( \frac{ 0.155 }{ 0.60 } - \frac{ 1 }{ 2500 } \right) }^{ -1 }$$

Evaluate

$$\frac{15000}{3869}\approx 3.876970793$$

Solution Steps

Expand \frac{0.155}{0.6} by multiplying both numerator and the denominator by 1000.

$$\left(\frac{155}{600}-\frac{1}{2500}\right)^{-1}$$

Reduce the fraction \frac{155}{600} to lowest terms by extracting and canceling out 5.

$$\left(\frac{31}{120}-\frac{1}{2500}\right)^{-1}$$

Subtract \frac{1}{2500} from \frac{31}{120} to get \frac{3869}{15000}.

$$\left(\frac{3869}{15000}\right)^{-1}$$

Calculate \frac{3869}{15000} to the power of -1 and get \frac{15000}{3869}.

$$\frac{15000}{3869}$$

Factor

$$\frac{3 \cdot 2 ^ {3} \cdot 5 ^ {4}}{53 \cdot 73} = 3\frac{3393}{3869} = 3.8769707934866893$$