Solve (3/8)^15*(4/9)^15:(1/6)^11

$$( \frac { 3 } { 8 } ) ^ { 15 } \cdot ( \frac { 4 } { 9 } ) ^ { 15 } : ( \frac { 1 } { 6 } ) ^ { 11 }$$

Evaluate

$$\frac{1}{1296}\approx 0.000771605$$

Solution Steps

Calculate \frac{3}{8} to the power of 15 and get \frac{14348907}{35184372088832}.

$$\frac{\frac{14348907}{35184372088832}\times \left(\frac{4}{9}\right)^{15}}{\left(\frac{1}{6}\right)^{11}}$$

Calculate \frac{4}{9} to the power of 15 and get \frac{1073741824}{205891132094649}.

$$\frac{\frac{14348907}{35184372088832}\times \frac{1073741824}{205891132094649}}{\left(\frac{1}{6}\right)^{11}}$$

Multiply \frac{14348907}{35184372088832} times \frac{1073741824}{205891132094649} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{14348907\times 1073741824}{35184372088832\times 205891132094649}}{\left(\frac{1}{6}\right)^{11}}$$

Do the multiplications in the fraction \frac{14348907\times 1073741824}{35184372088832\times 205891132094649}.

$$\frac{\frac{15407021574586368}{7244150201408990671659859968}}{\left(\frac{1}{6}\right)^{11}}$$

Reduce the fraction \frac{15407021574586368}{7244150201408990671659859968} to lowest terms by extracting and canceling out 15407021574586368.

$$\frac{\frac{1}{470184984576}}{\left(\frac{1}{6}\right)^{11}}$$

Calculate \frac{1}{6} to the power of 11 and get \frac{1}{362797056}.

$$\frac{\frac{1}{470184984576}}{\frac{1}{362797056}}$$

Divide \frac{1}{470184984576} by \frac{1}{362797056} by multiplying \frac{1}{470184984576} by the reciprocal of \frac{1}{362797056}.

$$\frac{1}{470184984576}\times 362797056$$

Multiply \frac{1}{470184984576} and 362797056 to get \frac{362797056}{470184984576}.

$$\frac{362797056}{470184984576}$$

Reduce the fraction \frac{362797056}{470184984576} to lowest terms by extracting and canceling out 362797056.

$$\frac{1}{1296}$$

Factor

$$\frac{1}{2 ^ {4} \cdot 3 ^ {4}} = 0.0007716049382716049$$