Solve {[(3^{2}+11):2^{2}]^{2}:5-1}*2^3-[7^2:(2*3+1)+2^3+10^0]+18:3=10

$$\{ [ ( 3 ^ { 2 } + 11 ) : 2 ^ { 2 } ] ^ { 2 } : 5 - 1 \} \cdot 2 ^ { 3 } - [ 7 ^ { 2 } : ( 2 \cdot 3 + 1 ) + 2 ^ { 3 } + 10 ^ { 0 } ] + 18 : 3 = 10$$

Verify

Solution Steps

Multiply both sides of the equation by 15, the least common multiple of 5,3.

$$15\left(\left(\frac{\left(\frac{3^{2}+11}{2^{2}}\right)^{2}}{5}-1\right)\times 2^{3}-\left(\frac{7^{2}}{2\times 3+1}+2^{3}+10^{0}\right)\right)+5\times 18=150$$

Calculate 3 to the power of 2 and get 9.

$$15\left(\left(\frac{\left(\frac{9+11}{2^{2}}\right)^{2}}{5}-1\right)\times 2^{3}-\left(\frac{7^{2}}{2\times 3+1}+2^{3}+10^{0}\right)\right)+5\times 18=150$$

Add 9 and 11 to get 20.

$$15\left(\left(\frac{\left(\frac{20}{2^{2}}\right)^{2}}{5}-1\right)\times 2^{3}-\left(\frac{7^{2}}{2\times 3+1}+2^{3}+10^{0}\right)\right)+5\times 18=150$$

Calculate 2 to the power of 2 and get 4.

$$15\left(\left(\frac{\left(\frac{20}{4}\right)^{2}}{5}-1\right)\times 2^{3}-\left(\frac{7^{2}}{2\times 3+1}+2^{3}+10^{0}\right)\right)+5\times 18=150$$

Divide 20 by 4 to get 5.

$$15\left(\left(\frac{5^{2}}{5}-1\right)\times 2^{3}-\left(\frac{7^{2}}{2\times 3+1}+2^{3}+10^{0}\right)\right)+5\times 18=150$$

Calculate 5 to the power of 2 and get 25.

$$15\left(\left(\frac{25}{5}-1\right)\times 2^{3}-\left(\frac{7^{2}}{2\times 3+1}+2^{3}+10^{0}\right)\right)+5\times 18=150$$

Divide 25 by 5 to get 5.

$$15\left(\left(5-1\right)\times 2^{3}-\left(\frac{7^{2}}{2\times 3+1}+2^{3}+10^{0}\right)\right)+5\times 18=150$$

Subtract 1 from 5 to get 4.

$$15\left(4\times 2^{3}-\left(\frac{7^{2}}{2\times 3+1}+2^{3}+10^{0}\right)\right)+5\times 18=150$$

Calculate 2 to the power of 3 and get 8.

$$15\left(4\times 8-\left(\frac{7^{2}}{2\times 3+1}+2^{3}+10^{0}\right)\right)+5\times 18=150$$

Multiply 4 and 8 to get 32.

$$15\left(32-\left(\frac{7^{2}}{2\times 3+1}+2^{3}+10^{0}\right)\right)+5\times 18=150$$

Calculate 7 to the power of 2 and get 49.

$$15\left(32-\left(\frac{49}{2\times 3+1}+2^{3}+10^{0}\right)\right)+5\times 18=150$$

Multiply 2 and 3 to get 6.

$$15\left(32-\left(\frac{49}{6+1}+2^{3}+10^{0}\right)\right)+5\times 18=150$$

Add 6 and 1 to get 7.

$$15\left(32-\left(\frac{49}{7}+2^{3}+10^{0}\right)\right)+5\times 18=150$$

Divide 49 by 7 to get 7.

$$15\left(32-\left(7+2^{3}+10^{0}\right)\right)+5\times 18=150$$

Calculate 2 to the power of 3 and get 8.

$$15\left(32-\left(7+8+10^{0}\right)\right)+5\times 18=150$$

Add 7 and 8 to get 15.

$$15\left(32-\left(15+10^{0}\right)\right)+5\times 18=150$$

Calculate 10 to the power of 0 and get 1.

$$15\left(32-\left(15+1\right)\right)+5\times 18=150$$

Add 15 and 1 to get 16.

$$15\left(32-16\right)+5\times 18=150$$

Subtract 16 from 32 to get 16.

$$15\times 16+5\times 18=150$$

Multiply 15 and 16 to get 240.

$$240+5\times 18=150$$

Multiply 5 and 18 to get 90.

$$240+90=150$$

Add 240 and 90 to get 330.

$$330=150$$

Compare 330 and 150.

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