Solve (19^4+1/4)/(20^4+frac{1{4})}

$$\frac { ( 19 ^ { 4 } + \frac { 1 } { 4 } ) } { ( 20 ^ { 4 } + \frac { 1 } { 4 } ) }$$

Evaluate

$$\frac{685}{841}\approx 0.81450654$$

Solution Steps

Calculate 19 to the power of 4 and get 130321.

$$\frac{130321+\frac{1}{4}}{20^{4}+\frac{1}{4}}$$

Convert 130321 to fraction \frac{521284}{4}.

$$\frac{\frac{521284}{4}+\frac{1}{4}}{20^{4}+\frac{1}{4}}$$

Since \frac{521284}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{521284+1}{4}}{20^{4}+\frac{1}{4}}$$

Add 521284 and 1 to get 521285.

$$\frac{\frac{521285}{4}}{20^{4}+\frac{1}{4}}$$

Calculate 20 to the power of 4 and get 160000.

$$\frac{\frac{521285}{4}}{160000+\frac{1}{4}}$$

Convert 160000 to fraction \frac{640000}{4}.

$$\frac{\frac{521285}{4}}{\frac{640000}{4}+\frac{1}{4}}$$

Since \frac{640000}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{521285}{4}}{\frac{640000+1}{4}}$$

Add 640000 and 1 to get 640001.

$$\frac{\frac{521285}{4}}{\frac{640001}{4}}$$

Divide \frac{521285}{4} by \frac{640001}{4} by multiplying \frac{521285}{4} by the reciprocal of \frac{640001}{4}.

$$\frac{521285}{4}\times \frac{4}{640001}$$

Multiply \frac{521285}{4} times \frac{4}{640001} by multiplying numerator times numerator and denominator times denominator.

$$\frac{521285\times 4}{4\times 640001}$$

Cancel out 4 in both numerator and denominator.

$$\frac{521285}{640001}$$

Reduce the fraction \frac{521285}{640001} to lowest terms by extracting and canceling out 761.

$$\frac{685}{841}$$

Factor

$$\frac{5 \cdot 137}{29 ^ {2}} = 0.8145065398335315$$