Solve left(3^4+1/4right)/left(2^4+frac{1{4}right)}

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

Evaluate

$$5$$

Solution Steps

Calculate 3 to the power of 4 and get 81.

$$\frac{81+\frac{1}{4}}{2^{4}+\frac{1}{4}}$$

Convert 81 to fraction \frac{324}{4}.

$$\frac{\frac{324}{4}+\frac{1}{4}}{2^{4}+\frac{1}{4}}$$

Since \frac{324}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{324+1}{4}}{2^{4}+\frac{1}{4}}$$

Add 324 and 1 to get 325.

$$\frac{\frac{325}{4}}{2^{4}+\frac{1}{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{\frac{325}{4}}{16+\frac{1}{4}}$$

Convert 16 to fraction \frac{64}{4}.

$$\frac{\frac{325}{4}}{\frac{64}{4}+\frac{1}{4}}$$

Since \frac{64}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{325}{4}}{\frac{64+1}{4}}$$

Add 64 and 1 to get 65.

$$\frac{\frac{325}{4}}{\frac{65}{4}}$$

Divide \frac{325}{4} by \frac{65}{4} by multiplying \frac{325}{4} by the reciprocal of \frac{65}{4}.

$$\frac{325}{4}\times \frac{4}{65}$$

Multiply \frac{325}{4} times \frac{4}{65} by multiplying numerator times numerator and denominator times denominator.

$$\frac{325\times 4}{4\times 65}$$

Cancel out 4 in both numerator and denominator.

$$\frac{325}{65}$$

Divide 325 by 65 to get 5.

$$5$$

Factor

$$5$$