Solve {left(0.166/0.85-1/2500right)}^-1=

$${ \left( \frac{ 0.166 }{ 0.85 } - \frac{ 1 }{ 2500 } \right) }^{ -1 } =$$

Evaluate

$$\frac{42500}{8283}\approx 5.130991187$$

Solution Steps

Expand \frac{0.166}{0.85} by multiplying both numerator and the denominator by 1000.

$$\left(\frac{166}{850}-\frac{1}{2500}\right)^{-1}$$

Reduce the fraction \frac{166}{850} to lowest terms by extracting and canceling out 2.

$$\left(\frac{83}{425}-\frac{1}{2500}\right)^{-1}$$

Subtract \frac{1}{2500} from \frac{83}{425} to get \frac{8283}{42500}.

$$\left(\frac{8283}{42500}\right)^{-1}$$

Calculate \frac{8283}{42500} to the power of -1 and get \frac{42500}{8283}.

$$\frac{42500}{8283}$$

Factor

$$\frac{17 \cdot 2 ^ {2} \cdot 5 ^ {4}}{3 \cdot 11 \cdot 251} = 5\frac{1085}{8283} = 5.130991186768079$$