Solve 5^2/2^2-2^2/5^2

$$\frac{ { 5 }^{ 2 } }{ { 2 }^{ 2 } } - \frac{ { 2 }^{ 2 } }{ { 5 }^{ 2 } }$$

Evaluate

$$\frac{609}{100}=6.09$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\frac{25}{2^{2}}-\frac{2^{2}}{5^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{25}{4}-\frac{2^{2}}{5^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{25}{4}-\frac{4}{5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25}{4}-\frac{4}{25}$$

Least common multiple of 4 and 25 is 100. Convert \frac{25}{4} and \frac{4}{25} to fractions with denominator 100.

$$\frac{625}{100}-\frac{16}{100}$$

Since \frac{625}{100} and \frac{16}{100} have the same denominator, subtract them by subtracting their numerators.

$$\frac{625-16}{100}$$

Subtract 16 from 625 to get 609.

$$\frac{609}{100}$$

Factor

$$\frac{3 \cdot 7 \cdot 29}{2 ^ {2} \cdot 5 ^ {2}} = 6\frac{9}{100} = 6.09$$