Solve +4^{2}+4^{3}-2^{3}+sqrt{21-2*5-2}-sqrt{(2^2)^3+3^2-6*2^3}

$$+ 4 ^ { 2 } + 4 ^ { 3 } - 2 ^ { 3 } + \sqrt { 21 - 2 \times 5 - 2 } - \sqrt { ( 2 ^ { 2 } ) ^ { 3 } + 3 ^ { 2 } - 6 \times 2 ^ { 3 } }$$

Evaluate

$$70$$

Solution Steps

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

$$4^{2}+4^{3}-2^{3}+\sqrt{21-2\times 5-2}-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Calculate 4 to the power of 2 and get 16.

$$16+4^{3}-2^{3}+\sqrt{21-2\times 5-2}-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Calculate 4 to the power of 3 and get 64.

$$16+64-2^{3}+\sqrt{21-2\times 5-2}-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Add 16 and 64 to get 80.

$$80-2^{3}+\sqrt{21-2\times 5-2}-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$80-8+\sqrt{21-2\times 5-2}-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Subtract 8 from 80 to get 72.

$$72+\sqrt{21-2\times 5-2}-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Multiply 2 and 5 to get 10.

$$72+\sqrt{21-10-2}-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Subtract 10 from 21 to get 11.

$$72+\sqrt{11-2}-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Subtract 2 from 11 to get 9.

$$72+\sqrt{9}-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Calculate the square root of 9 and get 3.

$$72+3-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Add 72 and 3 to get 75.

$$75-\sqrt{2^{6}+3^{2}-6\times 2^{3}}$$

Calculate 2 to the power of 6 and get 64.

$$75-\sqrt{64+3^{2}-6\times 2^{3}}$$

Calculate 3 to the power of 2 and get 9.

$$75-\sqrt{64+9-6\times 2^{3}}$$

Add 64 and 9 to get 73.

$$75-\sqrt{73-6\times 2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$75-\sqrt{73-6\times 8}$$

Multiply 6 and 8 to get 48.

$$75-\sqrt{73-48}$$

Subtract 48 from 73 to get 25.

$$75-\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$75-5$$

Subtract 5 from 75 to get 70.

$$70$$

Factor

$$2\times 5\times 7$$