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

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

Evaluate

$$\frac{11832592569282330623971439}{44079842304000000}\approx 268435456$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\left(\frac{160^{4}}{200^{2}}\right)^{2}-\left(\frac{13^{2}\times 5}{\left(180^{2}\right)^{2}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\left(\frac{160^{4}}{200^{2}}\right)^{2}-\left(\frac{13^{2}\times 5}{180^{4}}\right)^{2}$$

Calculate 160 to the power of 4 and get 655360000.

$$\left(\frac{655360000}{200^{2}}\right)^{2}-\left(\frac{13^{2}\times 5}{180^{4}}\right)^{2}$$

Calculate 200 to the power of 2 and get 40000.

$$\left(\frac{655360000}{40000}\right)^{2}-\left(\frac{13^{2}\times 5}{180^{4}}\right)^{2}$$

Divide 655360000 by 40000 to get 16384.

$$16384^{2}-\left(\frac{13^{2}\times 5}{180^{4}}\right)^{2}$$

Calculate 16384 to the power of 2 and get 268435456.

$$268435456-\left(\frac{13^{2}\times 5}{180^{4}}\right)^{2}$$

Calculate 13 to the power of 2 and get 169.

$$268435456-\left(\frac{169\times 5}{180^{4}}\right)^{2}$$

Multiply 169 and 5 to get 845.

$$268435456-\left(\frac{845}{180^{4}}\right)^{2}$$

Calculate 180 to the power of 4 and get 1049760000.

$$268435456-\left(\frac{845}{1049760000}\right)^{2}$$

Reduce the fraction \frac{845}{1049760000} to lowest terms by extracting and canceling out 5.

$$268435456-\left(\frac{169}{209952000}\right)^{2}$$

Calculate \frac{169}{209952000} to the power of 2 and get \frac{28561}{44079842304000000}.

$$268435456-\frac{28561}{44079842304000000}$$

Subtract \frac{28561}{44079842304000000} from 268435456 to get \frac{11832592569282330623971439}{44079842304000000}.

$$\frac{11832592569282330623971439}{44079842304000000}$$