Solve {left(160/200right)}^2-{left(13^25/180right)}^2

$${ \left( \frac{ 160 }{ 200 } \right) }^{ 2 } - { \left( \frac{ { 13 }^{ 2 } 5 }{ 180 } \right) }^{ 2 }$$

Evaluate

$$-\frac{693289}{32400}\approx -21.397808642$$

Solution Steps

Reduce the fraction \frac{160}{200} to lowest terms by extracting and canceling out 40.

$$\left(\frac{4}{5}\right)^{2}-\left(\frac{13^{2}\times 5}{180}\right)^{2}$$

Calculate \frac{4}{5} to the power of 2 and get \frac{16}{25}.

$$\frac{16}{25}-\left(\frac{13^{2}\times 5}{180}\right)^{2}$$

Calculate 13 to the power of 2 and get 169.

$$\frac{16}{25}-\left(\frac{169\times 5}{180}\right)^{2}$$

Multiply 169 and 5 to get 845.

$$\frac{16}{25}-\left(\frac{845}{180}\right)^{2}$$

Reduce the fraction \frac{845}{180} to lowest terms by extracting and canceling out 5.

$$\frac{16}{25}-\left(\frac{169}{36}\right)^{2}$$

Calculate \frac{169}{36} to the power of 2 and get \frac{28561}{1296}.

$$\frac{16}{25}-\frac{28561}{1296}$$

Subtract \frac{28561}{1296} from \frac{16}{25} to get -\frac{693289}{32400}.

$$-\frac{693289}{32400}$$

Factor

$$-\frac{693289}{32400} = -21\frac{12889}{32400} = -21.39780864197531$$