Solve (3^{2}*2)^{2}:(3^{2}*2)+[3^{3}*2:(2*7^{2}:7+2^2)]^3:3^3+2^2*2

$$( 3 ^ { 2 } \times 2 ) ^ { 2 } : ( 3 ^ { 2 } \times 2 ) + [ 3 ^ { 3 } \times 2 : ( 2 \times 7 ^ { 2 } : 7 + 2 ^ { 2 } ) ] ^ { 3 } : 3 ^ { 3 } + 2 ^ { 2 } \times 2$$

Evaluate

$$27$$

Solution Steps

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

$$\left(3^{2}\times 2\right)^{1}+\frac{\left(\frac{3^{3}\times 2}{\frac{2\times 7^{2}}{7}+2^{2}}\right)^{3}}{3^{3}}+2^{2}\times 2$$

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

$$\left(3^{2}\times 2\right)^{1}+\frac{\left(\frac{3^{3}\times 2}{\frac{2\times 7^{2}}{7}+2^{2}}\right)^{3}}{3^{3}}+2^{3}$$

Calculate 3 to the power of 2 and get 9.

$$\left(9\times 2\right)^{1}+\frac{\left(\frac{3^{3}\times 2}{\frac{2\times 7^{2}}{7}+2^{2}}\right)^{3}}{3^{3}}+2^{3}$$

Multiply 9 and 2 to get 18.

$$18^{1}+\frac{\left(\frac{3^{3}\times 2}{\frac{2\times 7^{2}}{7}+2^{2}}\right)^{3}}{3^{3}}+2^{3}$$

Calculate 18 to the power of 1 and get 18.

$$18+\frac{\left(\frac{3^{3}\times 2}{\frac{2\times 7^{2}}{7}+2^{2}}\right)^{3}}{3^{3}}+2^{3}$$

Calculate 3 to the power of 3 and get 27.

$$18+\frac{\left(\frac{27\times 2}{\frac{2\times 7^{2}}{7}+2^{2}}\right)^{3}}{3^{3}}+2^{3}$$

Multiply 27 and 2 to get 54.

$$18+\frac{\left(\frac{54}{\frac{2\times 7^{2}}{7}+2^{2}}\right)^{3}}{3^{3}}+2^{3}$$

Calculate 7 to the power of 2 and get 49.

$$18+\frac{\left(\frac{54}{\frac{2\times 49}{7}+2^{2}}\right)^{3}}{3^{3}}+2^{3}$$

Multiply 2 and 49 to get 98.

$$18+\frac{\left(\frac{54}{\frac{98}{7}+2^{2}}\right)^{3}}{3^{3}}+2^{3}$$

Divide 98 by 7 to get 14.

$$18+\frac{\left(\frac{54}{14+2^{2}}\right)^{3}}{3^{3}}+2^{3}$$

Calculate 2 to the power of 2 and get 4.

$$18+\frac{\left(\frac{54}{14+4}\right)^{3}}{3^{3}}+2^{3}$$

Add 14 and 4 to get 18.

$$18+\frac{\left(\frac{54}{18}\right)^{3}}{3^{3}}+2^{3}$$

Divide 54 by 18 to get 3.

$$18+\frac{3^{3}}{3^{3}}+2^{3}$$

Calculate 3 to the power of 3 and get 27.

$$18+\frac{27}{3^{3}}+2^{3}$$

Calculate 3 to the power of 3 and get 27.

$$18+\frac{27}{27}+2^{3}$$

Divide 27 by 27 to get 1.

$$18+1+2^{3}$$

Add 18 and 1 to get 19.

$$19+2^{3}$$

Calculate 2 to the power of 3 and get 8.

$$19+8$$

Add 19 and 8 to get 27.

$$27$$

Factor

$$3^{3}$$