Solve {[8^2+12-28:(4+3)-2^2*2^3]:10}^2:8=2

$$\{ [ 8 ^ { 2 } + 12 - 28 : ( 4 + 3 ) - 2 ^ { 2 } \times 2 ^ { 3 } ] : 10 \} ^ { 2 } : 8 = 2$$

Verify

Solution Steps

Multiply both sides of the equation by 8.

$$\left(\frac{8^{2}+12-\frac{28}{4+3}-2^{2}\times 2^{3}}{10}\right)^{2}=16$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\left(\frac{8^{2}+12-\frac{28}{4+3}-2^{5}}{10}\right)^{2}=16$$

Calculate 8 to the power of 2 and get 64.

$$\left(\frac{64+12-\frac{28}{4+3}-2^{5}}{10}\right)^{2}=16$$

Add 64 and 12 to get 76.

$$\left(\frac{76-\frac{28}{4+3}-2^{5}}{10}\right)^{2}=16$$

Add 4 and 3 to get 7.

$$\left(\frac{76-\frac{28}{7}-2^{5}}{10}\right)^{2}=16$$

Divide 28 by 7 to get 4.

$$\left(\frac{76-4-2^{5}}{10}\right)^{2}=16$$

Subtract 4 from 76 to get 72.

$$\left(\frac{72-2^{5}}{10}\right)^{2}=16$$

Calculate 2 to the power of 5 and get 32.

$$\left(\frac{72-32}{10}\right)^{2}=16$$

Subtract 32 from 72 to get 40.

$$\left(\frac{40}{10}\right)^{2}=16$$

Divide 40 by 10 to get 4.

$$4^{2}=16$$

Calculate 4 to the power of 2 and get 16.

$$16=16$$

Compare 16 and 16.

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