Solve (36:(6:2))^{3}-12^4}:(12^3)^2-[(36*6:2)^3

$$( 36 : ( 6 : 2 ) ) ^ { 3 } - 12 ^ { 4 } \} : ( 12 ^ { 3 } ) ^ { 2 } - [ ( 36 \cdot 6 : 2 ) ^ { 3 }$$

Evaluate

$$-19008$$

Solution Steps

Divide 36 by \frac{6}{2} by multiplying 36 by the reciprocal of \frac{6}{2}.

$$\left(\frac{36\times 2}{6}\right)^{3}-12^{4}$$

Multiply 36 and 2 to get 72.

$$\left(\frac{72}{6}\right)^{3}-12^{4}$$

Divide 72 by 6 to get 12.

$$12^{3}-12^{4}$$

Calculate 12 to the power of 3 and get 1728.

$$1728-12^{4}$$

Calculate 12 to the power of 4 and get 20736.

$$1728-20736$$

Subtract 20736 from 1728 to get -19008.

$$-19008$$

Factor

$$-19008$$