Solve {left(2^2divsqrt{16}right)}^10*{left(5^2divsqrt{625}right)}^10-{left(3^2divsqrt{81}right)}^10

$${ \left( { 2 }^{ 2 } \div \sqrt{ 16 } \right) }^{ 10 } \times { \left( { 5 }^{ 2 } \div \sqrt{ 625 } \right) }^{ 10 } - { \left( { 3 }^{ 2 } \div \sqrt{ 81 } \right) }^{ 10 }$$

Evaluate

$$0$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\left(\frac{4}{\sqrt{16}}\right)^{10}\times \left(\frac{5^{2}}{\sqrt{625}}\right)^{10}-\left(\frac{3^{2}}{\sqrt{81}}\right)^{10}$$

Calculate the square root of 16 and get 4.

$$\left(\frac{4}{4}\right)^{10}\times \left(\frac{5^{2}}{\sqrt{625}}\right)^{10}-\left(\frac{3^{2}}{\sqrt{81}}\right)^{10}$$

Divide 4 by 4 to get 1.

$$1^{10}\times \left(\frac{5^{2}}{\sqrt{625}}\right)^{10}-\left(\frac{3^{2}}{\sqrt{81}}\right)^{10}$$

Calculate 1 to the power of 10 and get 1.

$$1\times \left(\frac{5^{2}}{\sqrt{625}}\right)^{10}-\left(\frac{3^{2}}{\sqrt{81}}\right)^{10}$$

Calculate 5 to the power of 2 and get 25.

$$1\times \left(\frac{25}{\sqrt{625}}\right)^{10}-\left(\frac{3^{2}}{\sqrt{81}}\right)^{10}$$

Calculate the square root of 625 and get 25.

$$1\times \left(\frac{25}{25}\right)^{10}-\left(\frac{3^{2}}{\sqrt{81}}\right)^{10}$$

Divide 25 by 25 to get 1.

$$1\times 1^{10}-\left(\frac{3^{2}}{\sqrt{81}}\right)^{10}$$

Calculate 1 to the power of 10 and get 1.

$$1\times 1-\left(\frac{3^{2}}{\sqrt{81}}\right)^{10}$$

Multiply 1 and 1 to get 1.

$$1-\left(\frac{3^{2}}{\sqrt{81}}\right)^{10}$$

Calculate 3 to the power of 2 and get 9.

$$1-\left(\frac{9}{\sqrt{81}}\right)^{10}$$

Calculate the square root of 81 and get 9.

$$1-\left(\frac{9}{9}\right)^{10}$$

Divide 9 by 9 to get 1.

$$1-1^{10}$$

Calculate 1 to the power of 10 and get 1.

$$1-1$$

Subtract 1 from 1 to get 0.

$$0$$

Factor

$$0$$