Solve (6/5)^3*(-2/3)^4/(-frac{2{3})^2*(36/25)}=

$$\frac { ( \frac { 6 } { 5 } ) ^ { 3 } \times ( \frac { - 2 } { 3 } ) ^ { 4 } } { ( - \frac { 2 } { 3 } ) ^ { 2 } \times ( \frac { 36 } { 25 } ) } =$$

Evaluate

$$\frac{8}{15}\approx 0.533333333$$

Solution Steps

Calculate \frac{6}{5} to the power of 3 and get \frac{216}{125}.

$$\frac{\frac{216}{125}\times \left(\frac{-2}{3}\right)^{4}}{\left(-\frac{2}{3}\right)^{2}\times \frac{36}{25}}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$\frac{\frac{216}{125}\left(-\frac{2}{3}\right)^{4}}{\left(-\frac{2}{3}\right)^{2}\times \frac{36}{25}}$$

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

$$\frac{\frac{216}{125}\times \frac{16}{81}}{\left(-\frac{2}{3}\right)^{2}\times \frac{36}{25}}$$

Multiply \frac{216}{125} and \frac{16}{81} to get \frac{128}{375}.

$$\frac{\frac{128}{375}}{\left(-\frac{2}{3}\right)^{2}\times \frac{36}{25}}$$

Calculate -\frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$\frac{\frac{128}{375}}{\frac{4}{9}\times \frac{36}{25}}$$

Multiply \frac{4}{9} and \frac{36}{25} to get \frac{16}{25}.

$$\frac{\frac{128}{375}}{\frac{16}{25}}$$

Divide \frac{128}{375} by \frac{16}{25} by multiplying \frac{128}{375} by the reciprocal of \frac{16}{25}.

$$\frac{128}{375}\times \frac{25}{16}$$

Multiply \frac{128}{375} and \frac{25}{16} to get \frac{8}{15}.

$$\frac{8}{15}$$

Factor

$$\frac{2 ^ {3}}{3 \cdot 5} = 0.5333333333333333$$