Solve {left(495/496right)}^5-{left(594/595right)}^6

$${ \left( \frac{ 495 }{ 496 } \right) }^{ 5 } - { \left( \frac{ 594 }{ 595 } \right) }^{ 6 }$$

Evaluate

$$\frac{2236837135920760827073719}{1332018255130278239125504000000}\approx 0.000001679$$

Solution Steps

Calculate \frac{495}{496} to the power of 5 and get \frac{29718439059375}{30019840638976}.

$$\frac{29718439059375}{30019840638976}-\left(\frac{594}{595}\right)^{6}$$

Calculate \frac{594}{595} to the power of 6 and get \frac{43925697850453056}{44371263363765625}.

$$\frac{29718439059375}{30019840638976}-\frac{43925697850453056}{44371263363765625}$$

Least common multiple of 30019840638976 and 44371263363765625 is 1332018255130278239125504000000. Convert \frac{29718439059375}{30019840638976} and \frac{43925697850453056}{44371263363765625} to fractions with denominator 1332018255130278239125504000000.

$$\frac{1318644686263547299082958984375}{1332018255130278239125504000000}-\frac{1318642449426411378322131910656}{1332018255130278239125504000000}$$

Since \frac{1318644686263547299082958984375}{1332018255130278239125504000000} and \frac{1318642449426411378322131910656}{1332018255130278239125504000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1318644686263547299082958984375-1318642449426411378322131910656}{1332018255130278239125504000000}$$

Subtract 1318642449426411378322131910656 from 1318644686263547299082958984375 to get 2236837135920760827073719.

$$\frac{2236837135920760827073719}{1332018255130278239125504000000}$$

Factor

$$\frac{3 ^ {10} \cdot 11 ^ {5} \cdot 596861 \cdot 394080721}{2 ^ {20} \cdot 5 ^ {6} \cdot 7 ^ {6} \cdot 17 ^ {6} \cdot 31 ^ {5}} = 1.6792841444218696 \times 10^{-6}$$