Solve 1+4/2/4-frac{1{4}}*5+frac{2/{left(frac{1{2}right)}^2}}{{left(1/4right)}^4}

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

Evaluate

$$\frac{13312}{5}=2662.4$$

Solution Steps

Divide 4 by 2 to get 2.

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

Add 1 and 2 to get 3.

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

Convert 4 to fraction \frac{16}{4}.

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

Since \frac{16}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 16 to get 15.

$$\frac{3}{\frac{15}{4}}\times \frac{5+\frac{2}{\left(\frac{1}{2}\right)^{2}}}{\left(\frac{1}{4}\right)^{4}}$$

Divide 3 by \frac{15}{4} by multiplying 3 by the reciprocal of \frac{15}{4}.

$$3\times \frac{4}{15}\times \frac{5+\frac{2}{\left(\frac{1}{2}\right)^{2}}}{\left(\frac{1}{4}\right)^{4}}$$

Express 3\times \frac{4}{15} as a single fraction.

$$\frac{3\times 4}{15}\times \frac{5+\frac{2}{\left(\frac{1}{2}\right)^{2}}}{\left(\frac{1}{4}\right)^{4}}$$

Multiply 3 and 4 to get 12.

$$\frac{12}{15}\times \frac{5+\frac{2}{\left(\frac{1}{2}\right)^{2}}}{\left(\frac{1}{4}\right)^{4}}$$

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

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

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

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

Divide 2 by \frac{1}{4} by multiplying 2 by the reciprocal of \frac{1}{4}.

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

Multiply 2 and 4 to get 8.

$$\frac{4}{5}\times \frac{5+8}{\left(\frac{1}{4}\right)^{4}}$$

Add 5 and 8 to get 13.

$$\frac{4}{5}\times \frac{13}{\left(\frac{1}{4}\right)^{4}}$$

Calculate \frac{1}{4} to the power of 4 and get \frac{1}{256}.

$$\frac{4}{5}\times \frac{13}{\frac{1}{256}}$$

Divide 13 by \frac{1}{256} by multiplying 13 by the reciprocal of \frac{1}{256}.

$$\frac{4}{5}\times 13\times 256$$

Multiply 13 and 256 to get 3328.

$$\frac{4}{5}\times 3328$$

Express \frac{4}{5}\times 3328 as a single fraction.

$$\frac{4\times 3328}{5}$$

Multiply 4 and 3328 to get 13312.

$$\frac{13312}{5}$$

Factor

$$\frac{2 ^ {10} \cdot 13}{5} = 2662\frac{2}{5} = 2662.4$$