Solve 9/2^2*5^2-1/2*5^3

$$\frac { 9 } { 2 ^ { 2 } \cdot 5 ^ { 2 } } - \frac { 1 } { 2 \cdot 5 ^ { 3 } }$$

Evaluate

$$\frac{43}{500}=0.086$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\frac{9}{4\times 5^{2}}-\frac{1}{2\times 5^{3}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{9}{4\times 25}-\frac{1}{2\times 5^{3}}$$

Multiply 4 and 25 to get 100.

$$\frac{9}{100}-\frac{1}{2\times 5^{3}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{9}{100}-\frac{1}{2\times 125}$$

Multiply 2 and 125 to get 250.

$$\frac{9}{100}-\frac{1}{250}$$

Least common multiple of 100 and 250 is 500. Convert \frac{9}{100} and \frac{1}{250} to fractions with denominator 500.

$$\frac{45}{500}-\frac{2}{500}$$

Since \frac{45}{500} and \frac{2}{500} have the same denominator, subtract them by subtracting their numerators.

$$\frac{45-2}{500}$$

Subtract 2 from 45 to get 43.

$$\frac{43}{500}$$

Factor

$$\frac{43}{2 ^ {2} \cdot 5 ^ {3}} = 0.086$$