Solve {left(0.165/0.65-1/2500right)}^-1

$${ \left( \frac{ 0.165 }{ 0.65 } - \frac{ 1 }{ 2500 } \right) }^{ -1 }$$

Evaluate

$$\frac{32500}{8237}\approx 3.945611266$$

Solution Steps

Expand \frac{0.165}{0.65} by multiplying both numerator and the denominator by 1000.

$$\left(\frac{165}{650}-\frac{1}{2500}\right)^{-1}$$

Reduce the fraction \frac{165}{650} to lowest terms by extracting and canceling out 5.

$$\left(\frac{33}{130}-\frac{1}{2500}\right)^{-1}$$

Subtract \frac{1}{2500} from \frac{33}{130} to get \frac{8237}{32500}.

$$\left(\frac{8237}{32500}\right)^{-1}$$

Calculate \frac{8237}{32500} to the power of -1 and get \frac{32500}{8237}.

$$\frac{32500}{8237}$$

Factor

$$\frac{13 \cdot 2 ^ {2} \cdot 5 ^ {4}}{8237} = 3\frac{7789}{8237} = 3.945611266237708$$