Solve (-3/5)^2*(2/3)^4*(-5/6)^2

$$( - \frac { 3 } { 5 } ) ^ { 2 } \times ( \frac { 2 } { 3 } ) ^ { 4 } \times ( - \frac { 5 } { 6 } ) ^ { 2 }$$

Evaluate

$$\frac{4}{81}\approx 0.049382716$$

Solution Steps

Calculate -\frac{3}{5} to the power of 2 and get \frac{9}{25}.

$$\frac{9}{25}\times \left(\frac{2}{3}\right)^{4}\left(-\frac{5}{6}\right)^{2}$$

Calculate \frac{2}{3} to the power of 4 and get \frac{16}{81}.

$$\frac{9}{25}\times \frac{16}{81}\left(-\frac{5}{6}\right)^{2}$$

Multiply \frac{9}{25} times \frac{16}{81} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 16}{25\times 81}\left(-\frac{5}{6}\right)^{2}$$

Do the multiplications in the fraction \frac{9\times 16}{25\times 81}.

$$\frac{144}{2025}\left(-\frac{5}{6}\right)^{2}$$

Reduce the fraction \frac{144}{2025} to lowest terms by extracting and canceling out 9.

$$\frac{16}{225}\left(-\frac{5}{6}\right)^{2}$$

Calculate -\frac{5}{6} to the power of 2 and get \frac{25}{36}.

$$\frac{16}{225}\times \frac{25}{36}$$

Multiply \frac{16}{225} times \frac{25}{36} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16\times 25}{225\times 36}$$

Do the multiplications in the fraction \frac{16\times 25}{225\times 36}.

$$\frac{400}{8100}$$

Reduce the fraction \frac{400}{8100} to lowest terms by extracting and canceling out 100.

$$\frac{4}{81}$$

Factor

$$\frac{2 ^ {2}}{3 ^ {4}} = 0.04938271604938271$$