Solve (2^{5}+2^{4}+2^{4})*2^3+3^3*7-2^5*2^2-2

$$( 2 ^ { 5 } + 2 ^ { 4 } + 2 ^ { 4 } ) \times 2 ^ { 3 } + 3 ^ { 3 } \times 7 - 2 ^ { 5 } \times 2 ^ { 2 } - 2$$

Evaluate

$$571$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\left(2^{5}+2^{4}+2^{4}\right)\times 2^{3}+3^{3}\times 7-2^{7}-2$$

Calculate 2 to the power of 5 and get 32.

$$\left(32+2^{4}+2^{4}\right)\times 2^{3}+3^{3}\times 7-2^{7}-2$$

Calculate 2 to the power of 4 and get 16.

$$\left(32+16+2^{4}\right)\times 2^{3}+3^{3}\times 7-2^{7}-2$$

Add 32 and 16 to get 48.

$$\left(48+2^{4}\right)\times 2^{3}+3^{3}\times 7-2^{7}-2$$

Calculate 2 to the power of 4 and get 16.

$$\left(48+16\right)\times 2^{3}+3^{3}\times 7-2^{7}-2$$

Add 48 and 16 to get 64.

$$64\times 2^{3}+3^{3}\times 7-2^{7}-2$$

Calculate 2 to the power of 3 and get 8.

$$64\times 8+3^{3}\times 7-2^{7}-2$$

Multiply 64 and 8 to get 512.

$$512+3^{3}\times 7-2^{7}-2$$

Calculate 3 to the power of 3 and get 27.

$$512+27\times 7-2^{7}-2$$

Multiply 27 and 7 to get 189.

$$512+189-2^{7}-2$$

Add 512 and 189 to get 701.

$$701-2^{7}-2$$

Calculate 2 to the power of 7 and get 128.

$$701-128-2$$

Subtract 128 from 701 to get 573.

$$573-2$$

Subtract 2 from 573 to get 571.

$$571$$

Factor

$$571$$