Solve (3/2)^5div(3/2)^-3/(frac{4{5})^3}=

$$( \frac { 3 } { 2 } ) ^ { 5 } \div \frac { ( \frac { 3 } { 2 } ) ^ { - 3 } } { ( \frac { 4 } { 5 } ) ^ { 3 } } =$$

Evaluate

$$\frac{6561}{500}=13.122$$

Solution Steps

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

$$\frac{\frac{243}{32}}{\frac{\left(\frac{3}{2}\right)^{-3}}{\left(\frac{4}{5}\right)^{3}}}$$

Calculate \frac{3}{2} to the power of -3 and get \frac{8}{27}.

$$\frac{\frac{243}{32}}{\frac{\frac{8}{27}}{\left(\frac{4}{5}\right)^{3}}}$$

Calculate \frac{4}{5} to the power of 3 and get \frac{64}{125}.

$$\frac{\frac{243}{32}}{\frac{\frac{8}{27}}{\frac{64}{125}}}$$

Divide \frac{8}{27} by \frac{64}{125} by multiplying \frac{8}{27} by the reciprocal of \frac{64}{125}.

$$\frac{\frac{243}{32}}{\frac{8}{27}\times \frac{125}{64}}$$

Multiply \frac{8}{27} and \frac{125}{64} to get \frac{125}{216}.

$$\frac{\frac{243}{32}}{\frac{125}{216}}$$

Divide \frac{243}{32} by \frac{125}{216} by multiplying \frac{243}{32} by the reciprocal of \frac{125}{216}.

$$\frac{243}{32}\times \frac{216}{125}$$

Multiply \frac{243}{32} and \frac{216}{125} to get \frac{6561}{500}.

$$\frac{6561}{500}$$

Factor

$$\frac{3 ^ {8}}{2 ^ {2} \cdot 5 ^ {3}} = 13\frac{61}{500} = 13.122$$