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

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

Evaluate

$$\frac{128}{375}\approx 0.341333333$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and -3 to get 2.

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

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

$$\frac{\frac{9}{4}}{\frac{\left(\frac{3}{2}\right)^{3}}{\left(\frac{4}{5}\right)^{3}}}$$

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

$$\frac{\frac{9}{4}}{\frac{\frac{27}{8}}{\left(\frac{4}{5}\right)^{3}}}$$

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

$$\frac{\frac{9}{4}}{\frac{\frac{27}{8}}{\frac{64}{125}}}$$

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

$$\frac{\frac{9}{4}}{\frac{27}{8}\times \frac{125}{64}}$$

Multiply \frac{27}{8} and \frac{125}{64} to get \frac{3375}{512}.

$$\frac{\frac{9}{4}}{\frac{3375}{512}}$$

Divide \frac{9}{4} by \frac{3375}{512} by multiplying \frac{9}{4} by the reciprocal of \frac{3375}{512}.

$$\frac{9}{4}\times \frac{512}{3375}$$

Multiply \frac{9}{4} and \frac{512}{3375} to get \frac{128}{375}.

$$\frac{128}{375}$$

Factor

$$\frac{2 ^ {7}}{3 \cdot 5 ^ {3}} = 0.3413333333333333$$