Solve [3^{2}*3^{5}*(5*3-7*2^{2}+2)^{6}+7]^2-(3*5^2+2^4)+(6-2^2)

$$[ 3 ^ { 2 } \times 3 ^ { 5 } \cdot ( 5 \times 3 - 7 \times 2 ^ { 2 } + 2 ) ^ { 6 } + 7 ] ^ { 2 } - ( 3 \times 5 ^ { 2 } + 2 ^ { 4 } ) + ( 6 - 2 ^ { 2 } )$$

Evaluate

$$15011005688818519307$$

Solution Steps

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

$$\left(3^{7}\left(5\times 3-7\times 2^{2}+2\right)^{6}+7\right)^{2}-\left(3\times 5^{2}+2^{4}\right)+6-2^{2}$$

Calculate 3 to the power of 7 and get 2187.

$$\left(2187\left(5\times 3-7\times 2^{2}+2\right)^{6}+7\right)^{2}-\left(3\times 5^{2}+2^{4}\right)+6-2^{2}$$

Multiply 5 and 3 to get 15.

$$\left(2187\left(15-7\times 2^{2}+2\right)^{6}+7\right)^{2}-\left(3\times 5^{2}+2^{4}\right)+6-2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$\left(2187\left(15-7\times 4+2\right)^{6}+7\right)^{2}-\left(3\times 5^{2}+2^{4}\right)+6-2^{2}$$

Multiply 7 and 4 to get 28.

$$\left(2187\left(15-28+2\right)^{6}+7\right)^{2}-\left(3\times 5^{2}+2^{4}\right)+6-2^{2}$$

Subtract 28 from 15 to get -13.

$$\left(2187\left(-13+2\right)^{6}+7\right)^{2}-\left(3\times 5^{2}+2^{4}\right)+6-2^{2}$$

Add -13 and 2 to get -11.

$$\left(2187\left(-11\right)^{6}+7\right)^{2}-\left(3\times 5^{2}+2^{4}\right)+6-2^{2}$$

Calculate -11 to the power of 6 and get 1771561.

$$\left(2187\times 1771561+7\right)^{2}-\left(3\times 5^{2}+2^{4}\right)+6-2^{2}$$

Multiply 2187 and 1771561 to get 3874403907.

$$\left(3874403907+7\right)^{2}-\left(3\times 5^{2}+2^{4}\right)+6-2^{2}$$

Add 3874403907 and 7 to get 3874403914.

$$3874403914^{2}-\left(3\times 5^{2}+2^{4}\right)+6-2^{2}$$

Calculate 3874403914 to the power of 2 and get 15011005688818519396.

$$15011005688818519396-\left(3\times 5^{2}+2^{4}\right)+6-2^{2}$$

Calculate 5 to the power of 2 and get 25.

$$15011005688818519396-\left(3\times 25+2^{4}\right)+6-2^{2}$$

Multiply 3 and 25 to get 75.

$$15011005688818519396-\left(75+2^{4}\right)+6-2^{2}$$

Calculate 2 to the power of 4 and get 16.

$$15011005688818519396-\left(75+16\right)+6-2^{2}$$

Add 75 and 16 to get 91.

$$15011005688818519396-91+6-2^{2}$$

Subtract 91 from 15011005688818519396 to get 15011005688818519305.

$$15011005688818519305+6-2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$15011005688818519305+6-4$$

Subtract 4 from 6 to get 2.

$$15011005688818519305+2$$

Add 15011005688818519305 and 2 to get 15011005688818519307.

$$15011005688818519307$$

Factor

$$911\times 16477503500349637$$