Solve {c}{12-3^{4}*(6^{4}:2^{4})+3^{8}=12}{6^{2}-(4^2)^2:(2^4)=4^2}

$$\left. \begin{array} { c } { 12 - 3 ^ { 4 } \cdot ( 6 ^ { 4 } : 2 ^ { 4 } ) + 3 ^ { 8 } = 12 } \\ { 6 ^ { 2 } - ( 4 ^ { 2 } ) ^ { 2 } : ( 2 ^ { 4 } ) = 4 ^ { 2 } } \end{array} \right.$$

Verify

Solution Steps

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

$$12-3^{4}\times \frac{6^{4}}{2^{4}}+3^{8}=12\text{ and }6^{2}-\frac{4^{4}}{2^{4}}=4^{2}$$

Calculate 3 to the power of 4 and get 81.

$$12-81\times \frac{6^{4}}{2^{4}}+3^{8}=12\text{ and }6^{2}-\frac{4^{4}}{2^{4}}=4^{2}$$

Calculate 6 to the power of 4 and get 1296.

$$12-81\times \frac{1296}{2^{4}}+3^{8}=12\text{ and }6^{2}-\frac{4^{4}}{2^{4}}=4^{2}$$

Calculate 2 to the power of 4 and get 16.

$$12-81\times \frac{1296}{16}+3^{8}=12\text{ and }6^{2}-\frac{4^{4}}{2^{4}}=4^{2}$$

Divide 1296 by 16 to get 81.

$$12-81\times 81+3^{8}=12\text{ and }6^{2}-\frac{4^{4}}{2^{4}}=4^{2}$$

Multiply 81 and 81 to get 6561.

$$12-6561+3^{8}=12\text{ and }6^{2}-\frac{4^{4}}{2^{4}}=4^{2}$$

Subtract 6561 from 12 to get -6549.

$$-6549+3^{8}=12\text{ and }6^{2}-\frac{4^{4}}{2^{4}}=4^{2}$$

Calculate 3 to the power of 8 and get 6561.

$$-6549+6561=12\text{ and }6^{2}-\frac{4^{4}}{2^{4}}=4^{2}$$

Add -6549 and 6561 to get 12.

$$12=12\text{ and }6^{2}-\frac{4^{4}}{2^{4}}=4^{2}$$

Compare 12 and 12.

$$\text{true}\text{ and }6^{2}-\frac{4^{4}}{2^{4}}=4^{2}$$

Calculate 6 to the power of 2 and get 36.

$$\text{true}\text{ and }36-\frac{4^{4}}{2^{4}}=4^{2}$$

Calculate 4 to the power of 4 and get 256.

$$\text{true}\text{ and }36-\frac{256}{2^{4}}=4^{2}$$

Calculate 2 to the power of 4 and get 16.

$$\text{true}\text{ and }36-\frac{256}{16}=4^{2}$$

Divide 256 by 16 to get 16.

$$\text{true}\text{ and }36-16=4^{2}$$

Subtract 16 from 36 to get 20.

$$\text{true}\text{ and }20=4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$\text{true}\text{ and }20=16$$

Compare 20 and 16.

$$\text{true}\text{ and }\text{false}$$

The conjunction of \text{true} and \text{false} is \text{false}.

$$\text{false}$$