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

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

Evaluate

$$\frac{61}{25}=2.44$$

Solution Steps

Calculate 5 to the power of 4 and get 625.

$$\frac{625+\frac{1}{4}}{4^{4}+\frac{1}{4}}$$

Convert 625 to fraction \frac{2500}{4}.

$$\frac{\frac{2500}{4}+\frac{1}{4}}{4^{4}+\frac{1}{4}}$$

Since \frac{2500}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2500+1}{4}}{4^{4}+\frac{1}{4}}$$

Add 2500 and 1 to get 2501.

$$\frac{\frac{2501}{4}}{4^{4}+\frac{1}{4}}$$

Calculate 4 to the power of 4 and get 256.

$$\frac{\frac{2501}{4}}{256+\frac{1}{4}}$$

Convert 256 to fraction \frac{1024}{4}.

$$\frac{\frac{2501}{4}}{\frac{1024}{4}+\frac{1}{4}}$$

Since \frac{1024}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2501}{4}}{\frac{1024+1}{4}}$$

Add 1024 and 1 to get 1025.

$$\frac{\frac{2501}{4}}{\frac{1025}{4}}$$

Divide \frac{2501}{4} by \frac{1025}{4} by multiplying \frac{2501}{4} by the reciprocal of \frac{1025}{4}.

$$\frac{2501}{4}\times \frac{4}{1025}$$

Multiply \frac{2501}{4} times \frac{4}{1025} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2501\times 4}{4\times 1025}$$

Cancel out 4 in both numerator and denominator.

$$\frac{2501}{1025}$$

Reduce the fraction \frac{2501}{1025} to lowest terms by extracting and canceling out 41.

$$\frac{61}{25}$$

Factor

$$\frac{61}{5 ^ {2}} = 2\frac{11}{25} = 2.44$$