Solve {left(0.091/0.35-1/2500right)}^-1

$${ \left( \frac{ 0.091 }{ 0.35 } - \frac{ 1 }{ 2500 } \right) }^{ -1 }$$

Evaluate

$$\frac{2500}{649}\approx 3.852080123$$

Solution Steps

Expand \frac{0.091}{0.35} by multiplying both numerator and the denominator by 1000.

$$\left(\frac{91}{350}-\frac{1}{2500}\right)^{-1}$$

Reduce the fraction \frac{91}{350} to lowest terms by extracting and canceling out 7.

$$\left(\frac{13}{50}-\frac{1}{2500}\right)^{-1}$$

Subtract \frac{1}{2500} from \frac{13}{50} to get \frac{649}{2500}.

$$\left(\frac{649}{2500}\right)^{-1}$$

Calculate \frac{649}{2500} to the power of -1 and get \frac{2500}{649}.

$$\frac{2500}{649}$$

Factor

$$\frac{2 ^ {2} \cdot 5 ^ {4}}{11 \cdot 59} = 3\frac{553}{649} = 3.852080123266564$$