Solve {[(4^{3}-4^{2}):2-3*7]:3}^{3}+3*5-{[(2^{2})^{3}]^1}^2:(4^2*4^3)

$$\{ [ ( 4 ^ { 3 } - 4 ^ { 2 } ) : 2 - 3 \cdot 7 ] : 3 \} ^ { 3 } + 3 \cdot 5 - \{ [ ( 2 ^ { 2 } ) ^ { 3 } ] ^ { 1 } \} ^ { 2 } : ( 4 ^ { 2 } \cdot 4 ^ { 3 } )$$

Evaluate

$$12$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(\frac{\frac{4^{3}-4^{2}}{2}-3\times 7}{3}\right)^{3}+3\times 5-\frac{\left(\left(2^{6}\right)^{1}\right)^{2}}{4^{2}\times 4^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 1 to get 6.

$$\left(\frac{\frac{4^{3}-4^{2}}{2}-3\times 7}{3}\right)^{3}+3\times 5-\frac{\left(2^{6}\right)^{2}}{4^{2}\times 4^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\left(\frac{\frac{4^{3}-4^{2}}{2}-3\times 7}{3}\right)^{3}+3\times 5-\frac{2^{12}}{4^{2}\times 4^{3}}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\left(\frac{\frac{4^{3}-4^{2}}{2}-3\times 7}{3}\right)^{3}+3\times 5-\frac{2^{12}}{4^{5}}$$

Calculate 4 to the power of 3 and get 64.

$$\left(\frac{\frac{64-4^{2}}{2}-3\times 7}{3}\right)^{3}+3\times 5-\frac{2^{12}}{4^{5}}$$

Calculate 4 to the power of 2 and get 16.

$$\left(\frac{\frac{64-16}{2}-3\times 7}{3}\right)^{3}+3\times 5-\frac{2^{12}}{4^{5}}$$

Subtract 16 from 64 to get 48.

$$\left(\frac{\frac{48}{2}-3\times 7}{3}\right)^{3}+3\times 5-\frac{2^{12}}{4^{5}}$$

Divide 48 by 2 to get 24.

$$\left(\frac{24-3\times 7}{3}\right)^{3}+3\times 5-\frac{2^{12}}{4^{5}}$$

Multiply 3 and 7 to get 21.

$$\left(\frac{24-21}{3}\right)^{3}+3\times 5-\frac{2^{12}}{4^{5}}$$

Subtract 21 from 24 to get 3.

$$\left(\frac{3}{3}\right)^{3}+3\times 5-\frac{2^{12}}{4^{5}}$$

Divide 3 by 3 to get 1.

$$1^{3}+3\times 5-\frac{2^{12}}{4^{5}}$$

Calculate 1 to the power of 3 and get 1.

$$1+3\times 5-\frac{2^{12}}{4^{5}}$$

Multiply 3 and 5 to get 15.

$$1+15-\frac{2^{12}}{4^{5}}$$

Add 1 and 15 to get 16.

$$16-\frac{2^{12}}{4^{5}}$$

Calculate 2 to the power of 12 and get 4096.

$$16-\frac{4096}{4^{5}}$$

Calculate 4 to the power of 5 and get 1024.

$$16-\frac{4096}{1024}$$

Divide 4096 by 1024 to get 4.

$$16-4$$

Subtract 4 from 16 to get 12.

$$12$$

Factor

$$2^{2}\times 3$$