Solve [(4^{2}+4^{0})^{3}*(5^{2}-2^{3})^{2}-(2^{4}-4^{2}+3^{0})^2]^2:(8^2*2^2)

$$[ ( 4 ^ { 2 } + 4 ^ { 0 } ) ^ { 3 } \cdot ( 5 ^ { 2 } - 2 ^ { 3 } ) ^ { 2 } - ( 2 ^ { 4 } - 4 ^ { 2 } + 3 ^ { 0 } ) ^ { 2 } ] ^ { 2 } : ( 8 ^ { 2 } \times 2 ^ { 2 } )$$

Evaluate

$$7874965081$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\frac{\left(\left(16+4^{0}\right)^{3}\left(5^{2}-2^{3}\right)^{2}-\left(2^{4}-4^{2}+3^{0}\right)^{2}\right)^{2}}{8^{2}\times 2^{2}}$$

Calculate 4 to the power of 0 and get 1.

$$\frac{\left(\left(16+1\right)^{3}\left(5^{2}-2^{3}\right)^{2}-\left(2^{4}-4^{2}+3^{0}\right)^{2}\right)^{2}}{8^{2}\times 2^{2}}$$

Add 16 and 1 to get 17.

$$\frac{\left(17^{3}\left(5^{2}-2^{3}\right)^{2}-\left(2^{4}-4^{2}+3^{0}\right)^{2}\right)^{2}}{8^{2}\times 2^{2}}$$

Calculate 17 to the power of 3 and get 4913.

$$\frac{\left(4913\left(5^{2}-2^{3}\right)^{2}-\left(2^{4}-4^{2}+3^{0}\right)^{2}\right)^{2}}{8^{2}\times 2^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\left(4913\left(25-2^{3}\right)^{2}-\left(2^{4}-4^{2}+3^{0}\right)^{2}\right)^{2}}{8^{2}\times 2^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\left(4913\left(25-8\right)^{2}-\left(2^{4}-4^{2}+3^{0}\right)^{2}\right)^{2}}{8^{2}\times 2^{2}}$$

Subtract 8 from 25 to get 17.

$$\frac{\left(4913\times 17^{2}-\left(2^{4}-4^{2}+3^{0}\right)^{2}\right)^{2}}{8^{2}\times 2^{2}}$$

Calculate 17 to the power of 2 and get 289.

$$\frac{\left(4913\times 289-\left(2^{4}-4^{2}+3^{0}\right)^{2}\right)^{2}}{8^{2}\times 2^{2}}$$

Multiply 4913 and 289 to get 1419857.

$$\frac{\left(1419857-\left(2^{4}-4^{2}+3^{0}\right)^{2}\right)^{2}}{8^{2}\times 2^{2}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{\left(1419857-\left(16-4^{2}+3^{0}\right)^{2}\right)^{2}}{8^{2}\times 2^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{\left(1419857-\left(16-16+3^{0}\right)^{2}\right)^{2}}{8^{2}\times 2^{2}}$$

Subtract 16 from 16 to get 0.

$$\frac{\left(1419857-\left(0+3^{0}\right)^{2}\right)^{2}}{8^{2}\times 2^{2}}$$

Calculate 3 to the power of 0 and get 1.

$$\frac{\left(1419857-\left(0+1\right)^{2}\right)^{2}}{8^{2}\times 2^{2}}$$

Add 0 and 1 to get 1.

$$\frac{\left(1419857-1^{2}\right)^{2}}{8^{2}\times 2^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{\left(1419857-1\right)^{2}}{8^{2}\times 2^{2}}$$

Subtract 1 from 1419857 to get 1419856.

$$\frac{1419856^{2}}{8^{2}\times 2^{2}}$$

Calculate 1419856 to the power of 2 and get 2015991060736.

$$\frac{2015991060736}{8^{2}\times 2^{2}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{2015991060736}{64\times 2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{2015991060736}{64\times 4}$$

Multiply 64 and 4 to get 256.

$$\frac{2015991060736}{256}$$

Divide 2015991060736 by 256 to get 7874965081.

$$7874965081$$

Factor

$$88741^{2}$$