Solve 11/5^2*2^2-1/5*2^3

$$\frac { 11 } { 5 ^ { 2 } \cdot 2 ^ { 2 } } - \frac { 1 } { 5 \cdot 2 ^ { 3 } }$$

Evaluate

$$\frac{17}{200}=0.085$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\frac{11}{25\times 2^{2}}-\frac{1}{5\times 2^{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{11}{25\times 4}-\frac{1}{5\times 2^{3}}$$

Multiply 25 and 4 to get 100.

$$\frac{11}{100}-\frac{1}{5\times 2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{11}{100}-\frac{1}{5\times 8}$$

Multiply 5 and 8 to get 40.

$$\frac{11}{100}-\frac{1}{40}$$

Least common multiple of 100 and 40 is 200. Convert \frac{11}{100} and \frac{1}{40} to fractions with denominator 200.

$$\frac{22}{200}-\frac{5}{200}$$

Since \frac{22}{200} and \frac{5}{200} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22-5}{200}$$

Subtract 5 from 22 to get 17.

$$\frac{17}{200}$$

Factor

$$\frac{17}{2 ^ {3} \cdot 5 ^ {2}} = 0.085$$