Solve (2^2-2*1)(3^2-2*2)3^2*2*3(4^2-2*4)

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

Evaluate

$$4320$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Calculate 2 to the power of 2 and get 4.

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

Multiply 2 and 1 to get 2.

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

Subtract 2 from 4 to get 2.

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

Calculate 3 to the power of 2 and get 9.

$$2\left(9-2\times 2\right)\times 3^{3}\times 2\left(4^{2}-2\times 4\right)$$

Multiply 2 and 2 to get 4.

$$2\left(9-4\right)\times 3^{3}\times 2\left(4^{2}-2\times 4\right)$$

Subtract 4 from 9 to get 5.

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

Multiply 2 and 5 to get 10.

$$10\times 3^{3}\times 2\left(4^{2}-2\times 4\right)$$

Calculate 3 to the power of 3 and get 27.

$$10\times 27\times 2\left(4^{2}-2\times 4\right)$$

Multiply 10 and 27 to get 270.

$$270\times 2\left(4^{2}-2\times 4\right)$$

Multiply 270 and 2 to get 540.

$$540\left(4^{2}-2\times 4\right)$$

Calculate 4 to the power of 2 and get 16.

$$540\left(16-2\times 4\right)$$

Multiply 2 and 4 to get 8.

$$540\left(16-8\right)$$

Subtract 8 from 16 to get 8.

$$540\times 8$$

Multiply 540 and 8 to get 4320.

$$4320$$

Factor

$$2^{5}\times 3^{3}\times 5$$