Solve 100-frac{34^2/{left(5^3-4-5^24-2^25right)^4}}{3*4}

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

Evaluate

$$96$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

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

Multiply 3 and 16 to get 48.

$$100-\frac{\frac{48}{\left(5^{3}-4-5^{2}\times 4-2^{2}\times 5\right)^{4}}}{3\times 4}$$

Calculate 5 to the power of 3 and get 125.

$$100-\frac{\frac{48}{\left(125-4-5^{2}\times 4-2^{2}\times 5\right)^{4}}}{3\times 4}$$

Subtract 4 from 125 to get 121.

$$100-\frac{\frac{48}{\left(121-5^{2}\times 4-2^{2}\times 5\right)^{4}}}{3\times 4}$$

Calculate 5 to the power of 2 and get 25.

$$100-\frac{\frac{48}{\left(121-25\times 4-2^{2}\times 5\right)^{4}}}{3\times 4}$$

Multiply 25 and 4 to get 100.

$$100-\frac{\frac{48}{\left(121-100-2^{2}\times 5\right)^{4}}}{3\times 4}$$

Subtract 100 from 121 to get 21.

$$100-\frac{\frac{48}{\left(21-2^{2}\times 5\right)^{4}}}{3\times 4}$$

Calculate 2 to the power of 2 and get 4.

$$100-\frac{\frac{48}{\left(21-4\times 5\right)^{4}}}{3\times 4}$$

Multiply 4 and 5 to get 20.

$$100-\frac{\frac{48}{\left(21-20\right)^{4}}}{3\times 4}$$

Subtract 20 from 21 to get 1.

$$100-\frac{\frac{48}{1^{4}}}{3\times 4}$$

Calculate 1 to the power of 4 and get 1.

$$100-\frac{\frac{48}{1}}{3\times 4}$$

Anything divided by one gives itself.

$$100-\frac{48}{3\times 4}$$

Multiply 3 and 4 to get 12.

$$100-\frac{48}{12}$$

Divide 48 by 12 to get 4.

$$100-4$$

Subtract 4 from 100 to get 96.

$$96$$

Factor

$$2^{5}\times 3$$