Solve [(1^{2}+5^{1}:5-2)^{2}*(2^{2}*2^{2})^{2}+2*(2*2^{3}):2^3]^2:(1^2*2^2)

$$[ ( 1 ^ { 2 } + 5 ^ { 1 } : 5 - 2 ) ^ { 2 } \cdot ( 2 ^ { 2 } \cdot 2 ^ { 2 } ) ^ { 2 } + 2 \cdot ( 2 \cdot 2 ^ { 3 } ) : 2 ^ { 3 } ] ^ { 2 } : ( 1 ^ { 2 } \cdot 2 ^ { 2 } )$$

Evaluate

$$4$$

Solution Steps

Divide 5^{1} by 5 to get 1.

$$\frac{\left(\left(1^{2}+1-2\right)^{2}\times \left(2^{2}\times 2^{2}\right)^{2}+\frac{2\times 2\times 2^{3}}{2^{3}}\right)^{2}}{1^{2}\times 2^{2}}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

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

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

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

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 5 to get 2.

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

Calculate 1 to the power of 2 and get 1.

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

Add 1 and 1 to get 2.

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

Subtract 2 from 2 to get 0.

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

Calculate 0 to the power of 2 and get 0.

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

Calculate 2 to the power of 8 and get 256.

$$\frac{\left(0\times 256+2^{2}\right)^{2}}{1^{2}\times 2^{2}}$$

Multiply 0 and 256 to get 0.

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

Calculate 2 to the power of 2 and get 4.

$$\frac{\left(0+4\right)^{2}}{1^{2}\times 2^{2}}$$

Add 0 and 4 to get 4.

$$\frac{4^{2}}{1^{2}\times 2^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16}{1^{2}\times 2^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{16}{1\times 2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{16}{1\times 4}$$

Multiply 1 and 4 to get 4.

$$\frac{16}{4}$$

Divide 16 by 4 to get 4.

$$4$$

Factor

$$2^{2}$$