Solve [(2^{3})^{2}-3^{2}](5^{3}-5^2)+[4^2-(2^0+1)+5-2^3]

$$[ ( 2 ^ { 3 } ) ^ { 2 } - 3 ^ { 2 } ] ( 5 ^ { 3 } - 5 ^ { 2 } ) + [ 4 ^ { 2 } - ( 2 ^ { 0 } + 1 ) + 5 - 2 ^ { 3 } ]$$

Evaluate

$$5511$$

Solution Steps

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

$$\left(2^{6}-3^{2}\right)\left(5^{3}-5^{2}\right)+4^{2}-\left(2^{0}+1\right)+5-2^{3}$$

Calculate 2 to the power of 6 and get 64.

$$\left(64-3^{2}\right)\left(5^{3}-5^{2}\right)+4^{2}-\left(2^{0}+1\right)+5-2^{3}$$

Calculate 3 to the power of 2 and get 9.

$$\left(64-9\right)\left(5^{3}-5^{2}\right)+4^{2}-\left(2^{0}+1\right)+5-2^{3}$$

Subtract 9 from 64 to get 55.

$$55\left(5^{3}-5^{2}\right)+4^{2}-\left(2^{0}+1\right)+5-2^{3}$$

Calculate 5 to the power of 3 and get 125.

$$55\left(125-5^{2}\right)+4^{2}-\left(2^{0}+1\right)+5-2^{3}$$

Calculate 5 to the power of 2 and get 25.

$$55\left(125-25\right)+4^{2}-\left(2^{0}+1\right)+5-2^{3}$$

Subtract 25 from 125 to get 100.

$$55\times 100+4^{2}-\left(2^{0}+1\right)+5-2^{3}$$

Multiply 55 and 100 to get 5500.

$$5500+4^{2}-\left(2^{0}+1\right)+5-2^{3}$$

Calculate 4 to the power of 2 and get 16.

$$5500+16-\left(2^{0}+1\right)+5-2^{3}$$

Calculate 2 to the power of 0 and get 1.

$$5500+16-\left(1+1\right)+5-2^{3}$$

Add 1 and 1 to get 2.

$$5500+16-2+5-2^{3}$$

Subtract 2 from 16 to get 14.

$$5500+14+5-2^{3}$$

Add 14 and 5 to get 19.

$$5500+19-2^{3}$$

Calculate 2 to the power of 3 and get 8.

$$5500+19-8$$

Subtract 8 from 19 to get 11.

$$5500+11$$

Add 5500 and 11 to get 5511.

$$5511$$

Factor

$$3\times 11\times 167$$