Solve (5)(-9)sqrt{5}*(-2/3)^5*(1/3)^5

$$( 5 ) ( - 9 ) \sqrt { 5 } \times ( - \frac { 2 } { 3 } ) ^ { 5 } \times ( \frac { 1 } { 3 } ) ^ { 5 }$$

Evaluate

$$\frac{160\sqrt{5}}{6561}\approx 0.054529931$$

Solution Steps

Multiply 5 and -9 to get -45.

$$-45\sqrt{5}\left(-\frac{2}{3}\right)^{5}\times \left(\frac{1}{3}\right)^{5}$$

Calculate -\frac{2}{3} to the power of 5 and get -\frac{32}{243}.

$$-45\sqrt{5}\left(-\frac{32}{243}\right)\times \left(\frac{1}{3}\right)^{5}$$

Express -45\left(-\frac{32}{243}\right) as a single fraction.

$$\frac{-45\left(-32\right)}{243}\sqrt{5}\times \left(\frac{1}{3}\right)^{5}$$

Multiply -45 and -32 to get 1440.

$$\frac{1440}{243}\sqrt{5}\times \left(\frac{1}{3}\right)^{5}$$

Reduce the fraction \frac{1440}{243} to lowest terms by extracting and canceling out 9.

$$\frac{160}{27}\sqrt{5}\times \left(\frac{1}{3}\right)^{5}$$

Calculate \frac{1}{3} to the power of 5 and get \frac{1}{243}.

$$\frac{160}{27}\sqrt{5}\times \frac{1}{243}$$

Multiply \frac{160}{27} times \frac{1}{243} by multiplying numerator times numerator and denominator times denominator.

$$\frac{160\times 1}{27\times 243}\sqrt{5}$$

Do the multiplications in the fraction \frac{160\times 1}{27\times 243}.

$$\frac{160}{6561}\sqrt{5}$$