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

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

Evaluate

$$\frac{2565726409}{282429536481}\approx 0.009084483$$

Solution Steps

Reduce the fraction \frac{9}{27} to lowest terms by extracting and canceling out 9.

$$\left(\frac{1}{3}\right)^{6}\times \left(\frac{37}{27}\right)^{6}$$

Calculate \frac{1}{3} to the power of 6 and get \frac{1}{729}.

$$\frac{1}{729}\times \left(\frac{37}{27}\right)^{6}$$

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

$$\frac{1}{729}\times \frac{2565726409}{387420489}$$

Multiply \frac{1}{729} and \frac{2565726409}{387420489} to get \frac{2565726409}{282429536481}.

$$\frac{2565726409}{282429536481}$$

Factor

$$\frac{37 ^ {6}}{3 ^ {24}} = 0.009084483304998113$$