Solve (14/31)^15*(31/14)^6*[(31/14)]^3

$$( \frac { 14 } { 31 } ) ^ { 15 } \times ( \frac { 31 } { 14 } ) ^ { 6 } \times [ ( \frac { 31 } { 14 } ) ] ^ { 3 }$$

Evaluate

$$\frac{7529536}{887503681}\approx 0.008483949$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\left(\frac{14}{31}\right)^{15}\times \left(\frac{31}{14}\right)^{9}$$

Calculate \frac{14}{31} to the power of 15 and get \frac{155568095557812224}{23465261991844685929951}.

$$\frac{155568095557812224}{23465261991844685929951}\times \left(\frac{31}{14}\right)^{9}$$

Calculate \frac{31}{14} to the power of 9 and get \frac{26439622160671}{20661046784}.

$$\frac{155568095557812224}{23465261991844685929951}\times \frac{26439622160671}{20661046784}$$

Multiply \frac{155568095557812224}{23465261991844685929951} times \frac{26439622160671}{20661046784} by multiplying numerator times numerator and denominator times denominator.

$$\frac{155568095557812224\times 26439622160671}{23465261991844685929951\times 20661046784}$$

Do the multiplications in the fraction \frac{155568095557812224\times 26439622160671}{23465261991844685929951\times 20661046784}.

$$\frac{4113161666803715830908575842304}{484816875812320082460504157827584}$$

Reduce the fraction \frac{4113161666803715830908575842304}{484816875812320082460504157827584} to lowest terms by extracting and canceling out 546270270412906695832064.

$$\frac{7529536}{887503681}$$

Factor

$$\frac{2 ^ {6} \cdot 7 ^ {6}}{31 ^ {6}} = 0.008483949037277288$$