Solve [5^-1-3(2)^-2]^-1

$$[ 5 ^ { - 1 } - 3 ( 2 ) ^ { - 2 } ] ^ { - 1 }$$

Evaluate

$$-\frac{20}{11}\approx -1.818181818$$

Solution Steps

Calculate 5 to the power of -1 and get \frac{1}{5}.

$$\left(\frac{1}{5}-3\times 2^{-2}\right)^{-1}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\left(\frac{1}{5}-3\times \frac{1}{4}\right)^{-1}$$

Multiply 3 and \frac{1}{4} to get \frac{3}{4}.

$$\left(\frac{1}{5}-\frac{3}{4}\right)^{-1}$$

Subtract \frac{3}{4} from \frac{1}{5} to get -\frac{11}{20}.

$$\left(-\frac{11}{20}\right)^{-1}$$

Calculate -\frac{11}{20} to the power of -1 and get -\frac{20}{11}.

$$-\frac{20}{11}$$

Factor

$$-\frac{20}{11} = -1\frac{9}{11} = -1.8181818181818181$$