Solve (1-3^{4})^{3}+(3^{6}-3^{3})(3^{6}+3^{3})-2*3^6(3^3-1)+3(3^4-1)^2

$$( 1 - 3 ^ { 4 } ) ^ { 3 } + ( 3 ^ { 6 } - 3 ^ { 3 } ) ( 3 ^ { 6 } + 3 ^ { 3 } ) - 2 \cdot 3 ^ { 6 } ( 3 ^ { 3 } - 1 ) + 3 ( 3 ^ { 4 } - 1 ) ^ { 2 }$$

Evaluate

$$4$$

Solution Steps

Calculate 3 to the power of 4 and get 81.

$$\left(1-81\right)^{3}+\left(3^{6}-3^{3}\right)\left(3^{6}+3^{3}\right)-2\times 3^{6}\left(3^{3}-1\right)+3\left(3^{4}-1\right)^{2}$$

Subtract 81 from 1 to get -80.

$$\left(-80\right)^{3}+\left(3^{6}-3^{3}\right)\left(3^{6}+3^{3}\right)-2\times 3^{6}\left(3^{3}-1\right)+3\left(3^{4}-1\right)^{2}$$

Calculate -80 to the power of 3 and get -512000.

$$-512000+\left(3^{6}-3^{3}\right)\left(3^{6}+3^{3}\right)-2\times 3^{6}\left(3^{3}-1\right)+3\left(3^{4}-1\right)^{2}$$

Calculate 3 to the power of 6 and get 729.

$$-512000+\left(729-3^{3}\right)\left(3^{6}+3^{3}\right)-2\times 3^{6}\left(3^{3}-1\right)+3\left(3^{4}-1\right)^{2}$$

Calculate 3 to the power of 3 and get 27.

$$-512000+\left(729-27\right)\left(3^{6}+3^{3}\right)-2\times 3^{6}\left(3^{3}-1\right)+3\left(3^{4}-1\right)^{2}$$

Subtract 27 from 729 to get 702.

$$-512000+702\left(3^{6}+3^{3}\right)-2\times 3^{6}\left(3^{3}-1\right)+3\left(3^{4}-1\right)^{2}$$

Calculate 3 to the power of 6 and get 729.

$$-512000+702\left(729+3^{3}\right)-2\times 3^{6}\left(3^{3}-1\right)+3\left(3^{4}-1\right)^{2}$$

Calculate 3 to the power of 3 and get 27.

$$-512000+702\left(729+27\right)-2\times 3^{6}\left(3^{3}-1\right)+3\left(3^{4}-1\right)^{2}$$

Add 729 and 27 to get 756.

$$-512000+702\times 756-2\times 3^{6}\left(3^{3}-1\right)+3\left(3^{4}-1\right)^{2}$$

Multiply 702 and 756 to get 530712.

$$-512000+530712-2\times 3^{6}\left(3^{3}-1\right)+3\left(3^{4}-1\right)^{2}$$

Add -512000 and 530712 to get 18712.

$$18712-2\times 3^{6}\left(3^{3}-1\right)+3\left(3^{4}-1\right)^{2}$$

Calculate 3 to the power of 6 and get 729.

$$18712-2\times 729\left(3^{3}-1\right)+3\left(3^{4}-1\right)^{2}$$

Multiply 2 and 729 to get 1458.

$$18712-1458\left(3^{3}-1\right)+3\left(3^{4}-1\right)^{2}$$

Calculate 3 to the power of 3 and get 27.

$$18712-1458\left(27-1\right)+3\left(3^{4}-1\right)^{2}$$

Subtract 1 from 27 to get 26.

$$18712-1458\times 26+3\left(3^{4}-1\right)^{2}$$

Multiply 1458 and 26 to get 37908.

$$18712-37908+3\left(3^{4}-1\right)^{2}$$

Subtract 37908 from 18712 to get -19196.

$$-19196+3\left(3^{4}-1\right)^{2}$$

Calculate 3 to the power of 4 and get 81.

$$-19196+3\left(81-1\right)^{2}$$

Subtract 1 from 81 to get 80.

$$-19196+3\times 80^{2}$$

Calculate 80 to the power of 2 and get 6400.

$$-19196+3\times 6400$$

Multiply 3 and 6400 to get 19200.

$$-19196+19200$$

Add -19196 and 19200 to get 4.

$$4$$

Factor

$$2^{2}$$