Solve (9/37)^6*(37/27)^6=

$$( \frac { 9 } { 37 } ) ^ { 6 } \cdot ( \frac { 37 } { 27 } ) ^ { 6 } =$$

Evaluate

$$\frac{1}{729}\approx 0.001371742$$

Solution Steps

Calculate \frac{9}{37} to the power of 6 and get \frac{531441}{2565726409}.

$$\frac{531441}{2565726409}\times \left(\frac{37}{27}\right)^{6}$$

Calculate \frac{37}{27} to the power of 6 and get \frac{2565726409}{387420489}.

$$\frac{531441}{2565726409}\times \frac{2565726409}{387420489}$$

Multiply \frac{531441}{2565726409} times \frac{2565726409}{387420489} by multiplying numerator times numerator and denominator times denominator.

$$\frac{531441\times 2565726409}{2565726409\times 387420489}$$

Cancel out 2565726409 in both numerator and denominator.

$$\frac{531441}{387420489}$$

Reduce the fraction \frac{531441}{387420489} to lowest terms by extracting and canceling out 531441.

$$\frac{1}{729}$$

Factor

$$\frac{1}{3 ^ {6}} = 0.0013717421124828531$$