Solve 100-3*4^{2}:(5^3-4-5^2*4-2^2*5)^4:3-4=

$$100 - 3 \cdot 4 ^ { 2 } : ( 5 ^ { 3 } - 4 - 5 ^ { 2 } \cdot 4 - 2 ^ { 2 } \cdot 5 ) ^ { 4 } : 3 - 4 =$$

Evaluate

$$80$$

Solution Steps

Express \frac{\frac{3\times 4^{2}}{\left(5^{3}-4-5^{2}\times 4-2^{2}\times 5\right)^{4}}}{3} as a single fraction.

$$100-\frac{3\times 4^{2}}{\left(5^{3}-4-5^{2}\times 4-2^{2}\times 5\right)^{4}\times 3}-4$$

Cancel out 3 in both numerator and denominator.

$$100-\frac{4^{2}}{\left(5^{3}-4-4\times 5^{2}-5\times 2^{2}\right)^{4}}-4$$

Calculate 4 to the power of 2 and get 16.

$$100-\frac{16}{\left(5^{3}-4-4\times 5^{2}-5\times 2^{2}\right)^{4}}-4$$

Calculate 5 to the power of 3 and get 125.

$$100-\frac{16}{\left(125-4-4\times 5^{2}-5\times 2^{2}\right)^{4}}-4$$

Subtract 4 from 125 to get 121.

$$100-\frac{16}{\left(121-4\times 5^{2}-5\times 2^{2}\right)^{4}}-4$$

Calculate 5 to the power of 2 and get 25.

$$100-\frac{16}{\left(121-4\times 25-5\times 2^{2}\right)^{4}}-4$$

Multiply 4 and 25 to get 100.

$$100-\frac{16}{\left(121-100-5\times 2^{2}\right)^{4}}-4$$

Subtract 100 from 121 to get 21.

$$100-\frac{16}{\left(21-5\times 2^{2}\right)^{4}}-4$$

Calculate 2 to the power of 2 and get 4.

$$100-\frac{16}{\left(21-5\times 4\right)^{4}}-4$$

Multiply 5 and 4 to get 20.

$$100-\frac{16}{\left(21-20\right)^{4}}-4$$

Subtract 20 from 21 to get 1.

$$100-\frac{16}{1^{4}}-4$$

Calculate 1 to the power of 4 and get 1.

$$100-\frac{16}{1}-4$$

Anything divided by one gives itself.

$$100-16-4$$

Subtract 16 from 100 to get 84.

$$84-4$$

Subtract 4 from 84 to get 80.

$$80$$

Factor

$$2^{4}\times 5$$