Solve (5^{2}*2:5)^{2}+(3^{2}*3^3:3^4)^4-12^2

$$( 5 ^ { 2 } \cdot 2 : 5 ) ^ { 2 } + ( 3 ^ { 2 } \cdot 3 ^ { 3 } : 3 ^ { 4 } ) ^ { 4 } - 12 ^ { 2 }$$

Evaluate

$$37$$

Solution Steps

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

$$\left(\frac{5^{2}\times 2}{5}\right)^{2}+\left(\frac{3^{5}}{3^{4}}\right)^{4}-12^{2}$$

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

$$\left(\frac{5^{2}\times 2}{5}\right)^{2}+\left(3^{1}\right)^{4}-12^{2}$$

To raise a power to another power, multiply the exponents. Multiply 1 and 4 to get 4.

$$\left(\frac{5^{2}\times 2}{5}\right)^{2}+3^{4}-12^{2}$$

Calculate 5 to the power of 2 and get 25.

$$\left(\frac{25\times 2}{5}\right)^{2}+3^{4}-12^{2}$$

Multiply 25 and 2 to get 50.

$$\left(\frac{50}{5}\right)^{2}+3^{4}-12^{2}$$

Divide 50 by 5 to get 10.

$$10^{2}+3^{4}-12^{2}$$

Calculate 10 to the power of 2 and get 100.

$$100+3^{4}-12^{2}$$

Calculate 3 to the power of 4 and get 81.

$$100+81-12^{2}$$

Add 100 and 81 to get 181.

$$181-12^{2}$$

Calculate 12 to the power of 2 and get 144.

$$181-144$$

Subtract 144 from 181 to get 37.

$$37$$

Factor

$$37$$