Solve 2^{2}*2*{10^{2}-[(4^{2}*2^{2}-8^{2}:2^{2})+4*(9^3:9^2+3^6:3^3):3+1]}

$$2 ^ { 2 } \times 2 \times \{ 10 ^ { 2 } - [ ( 4 ^ { 2 } \times 2 ^ { 2 } - 8 ^ { 2 } : 2 ^ { 2 } ) + 4 \times ( 9 ^ { 3 } : 9 ^ { 2 } + 3 ^ { 6 } : 3 ^ { 3 } ) : 3 + 1 ] \}$$

Evaluate

$$24$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 3 to get 1.

$$2^{2}\times 2\left(10^{2}-\left(4^{2}\times 2^{2}-\frac{8^{2}}{2^{2}}+\frac{4\left(9^{1}+\frac{3^{6}}{3^{3}}\right)}{3}+1\right)\right)$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 6 to get 3.

$$2^{2}\times 2\left(10^{2}-\left(4^{2}\times 2^{2}-\frac{8^{2}}{2^{2}}+\frac{4\left(9^{1}+3^{3}\right)}{3}+1\right)\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$2^{3}\left(10^{2}-\left(4^{2}\times 2^{2}-\frac{8^{2}}{2^{2}}+\frac{4\left(9^{1}+3^{3}\right)}{3}+1\right)\right)$$

Calculate 2 to the power of 3 and get 8.

$$8\left(10^{2}-\left(4^{2}\times 2^{2}-\frac{8^{2}}{2^{2}}+\frac{4\left(9^{1}+3^{3}\right)}{3}+1\right)\right)$$

Calculate 10 to the power of 2 and get 100.

$$8\left(100-\left(4^{2}\times 2^{2}-\frac{8^{2}}{2^{2}}+\frac{4\left(9^{1}+3^{3}\right)}{3}+1\right)\right)$$

Calculate 4 to the power of 2 and get 16.

$$8\left(100-\left(16\times 2^{2}-\frac{8^{2}}{2^{2}}+\frac{4\left(9^{1}+3^{3}\right)}{3}+1\right)\right)$$

Calculate 2 to the power of 2 and get 4.

$$8\left(100-\left(16\times 4-\frac{8^{2}}{2^{2}}+\frac{4\left(9^{1}+3^{3}\right)}{3}+1\right)\right)$$

Multiply 16 and 4 to get 64.

$$8\left(100-\left(64-\frac{8^{2}}{2^{2}}+\frac{4\left(9^{1}+3^{3}\right)}{3}+1\right)\right)$$

Calculate 8 to the power of 2 and get 64.

$$8\left(100-\left(64-\frac{64}{2^{2}}+\frac{4\left(9^{1}+3^{3}\right)}{3}+1\right)\right)$$

Calculate 2 to the power of 2 and get 4.

$$8\left(100-\left(64-\frac{64}{4}+\frac{4\left(9^{1}+3^{3}\right)}{3}+1\right)\right)$$

Divide 64 by 4 to get 16.

$$8\left(100-\left(64-16+\frac{4\left(9^{1}+3^{3}\right)}{3}+1\right)\right)$$

Subtract 16 from 64 to get 48.

$$8\left(100-\left(48+\frac{4\left(9^{1}+3^{3}\right)}{3}+1\right)\right)$$

Calculate 9 to the power of 1 and get 9.

$$8\left(100-\left(48+\frac{4\left(9+3^{3}\right)}{3}+1\right)\right)$$

Calculate 3 to the power of 3 and get 27.

$$8\left(100-\left(48+\frac{4\left(9+27\right)}{3}+1\right)\right)$$

Add 9 and 27 to get 36.

$$8\left(100-\left(48+\frac{4\times 36}{3}+1\right)\right)$$

Multiply 4 and 36 to get 144.

$$8\left(100-\left(48+\frac{144}{3}+1\right)\right)$$

Divide 144 by 3 to get 48.

$$8\left(100-\left(48+48+1\right)\right)$$

Add 48 and 48 to get 96.

$$8\left(100-\left(96+1\right)\right)$$

Add 96 and 1 to get 97.

$$8\left(100-97\right)$$

Subtract 97 from 100 to get 3.

$$8\times 3$$

Multiply 8 and 3 to get 24.

$$24$$

Factor

$$2^{3}\times 3$$