Solve 2^{4}+[3*2^{3}:6+2^{2}+3^{2}*(2^{5}:2^{4}+2^3):(30^2:5^2-6)]^2=

$$2 ^ { 4 } + [ 3 \times 2 ^ { 3 } : 6 + 2 ^ { 2 } + 3 ^ { 2 } \times ( 2 ^ { 5 } : 2 ^ { 4 } + 2 ^ { 3 } ) : ( 30 ^ { 2 } : 5 ^ { 2 } - 6 ) ] ^ { 2 } =$$

Evaluate

$$137$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 5 to get 1.

$$2^{4}+\left(\frac{3\times 2^{3}}{6}+2^{2}+\frac{3^{2}\left(2^{1}+2^{3}\right)}{\frac{30^{2}}{5^{2}}-6}\right)^{2}$$

Calculate 2 to the power of 4 and get 16.

$$16+\left(\frac{3\times 2^{3}}{6}+2^{2}+\frac{3^{2}\left(2^{1}+2^{3}\right)}{\frac{30^{2}}{5^{2}}-6}\right)^{2}$$

Calculate 2 to the power of 3 and get 8.

$$16+\left(\frac{3\times 8}{6}+2^{2}+\frac{3^{2}\left(2^{1}+2^{3}\right)}{\frac{30^{2}}{5^{2}}-6}\right)^{2}$$

Multiply 3 and 8 to get 24.

$$16+\left(\frac{24}{6}+2^{2}+\frac{3^{2}\left(2^{1}+2^{3}\right)}{\frac{30^{2}}{5^{2}}-6}\right)^{2}$$

Divide 24 by 6 to get 4.

$$16+\left(4+2^{2}+\frac{3^{2}\left(2^{1}+2^{3}\right)}{\frac{30^{2}}{5^{2}}-6}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$16+\left(4+4+\frac{3^{2}\left(2^{1}+2^{3}\right)}{\frac{30^{2}}{5^{2}}-6}\right)^{2}$$

Add 4 and 4 to get 8.

$$16+\left(8+\frac{3^{2}\left(2^{1}+2^{3}\right)}{\frac{30^{2}}{5^{2}}-6}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$16+\left(8+\frac{9\left(2^{1}+2^{3}\right)}{\frac{30^{2}}{5^{2}}-6}\right)^{2}$$

Calculate 2 to the power of 1 and get 2.

$$16+\left(8+\frac{9\left(2+2^{3}\right)}{\frac{30^{2}}{5^{2}}-6}\right)^{2}$$

Calculate 2 to the power of 3 and get 8.

$$16+\left(8+\frac{9\left(2+8\right)}{\frac{30^{2}}{5^{2}}-6}\right)^{2}$$

Add 2 and 8 to get 10.

$$16+\left(8+\frac{9\times 10}{\frac{30^{2}}{5^{2}}-6}\right)^{2}$$

Multiply 9 and 10 to get 90.

$$16+\left(8+\frac{90}{\frac{30^{2}}{5^{2}}-6}\right)^{2}$$

Calculate 30 to the power of 2 and get 900.

$$16+\left(8+\frac{90}{\frac{900}{5^{2}}-6}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$16+\left(8+\frac{90}{\frac{900}{25}-6}\right)^{2}$$

Divide 900 by 25 to get 36.

$$16+\left(8+\frac{90}{36-6}\right)^{2}$$

Subtract 6 from 36 to get 30.

$$16+\left(8+\frac{90}{30}\right)^{2}$$

Divide 90 by 30 to get 3.

$$16+\left(8+3\right)^{2}$$

Add 8 and 3 to get 11.

$$16+11^{2}$$

Calculate 11 to the power of 2 and get 121.

$$16+121$$

Add 16 and 121 to get 137.

$$137$$

Factor

$$137$$