Solve (frac{3/2)^{2}(2/3)^{-2}(3/4)^-1}{(1/3)^4(-frac{1}{2})^-4(frac{1}{9})^3}

$$\frac { ( \frac { 3 } { 2 } ) ^ { 2 } ( \frac { 2 } { 3 } ) ^ { - 2 } ( \frac { 3 } { 4 } ) ^ { - 1 } } { ( \frac { 1 } { 3 } ) ^ { 4 } ( - \frac { 1 } { 2 } ) ^ { - 4 } ( \frac { 1 } { 9 } ) ^ { 3 } }$$

Evaluate

$$\frac{1594323}{64}=24911.296875$$

Solution Steps

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

$$\frac{\frac{9}{4}\times \left(\frac{2}{3}\right)^{-2}\times \left(\frac{3}{4}\right)^{-1}}{\left(\frac{1}{3}\right)^{4}\left(-\frac{1}{2}\right)^{-4}\times \left(\frac{1}{9}\right)^{3}}$$

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

$$\frac{\frac{9}{4}\times \frac{9}{4}\times \left(\frac{3}{4}\right)^{-1}}{\left(\frac{1}{3}\right)^{4}\left(-\frac{1}{2}\right)^{-4}\times \left(\frac{1}{9}\right)^{3}}$$

Multiply \frac{9}{4} and \frac{9}{4} to get \frac{81}{16}.

$$\frac{\frac{81}{16}\times \left(\frac{3}{4}\right)^{-1}}{\left(\frac{1}{3}\right)^{4}\left(-\frac{1}{2}\right)^{-4}\times \left(\frac{1}{9}\right)^{3}}$$

Calculate \frac{3}{4} to the power of -1 and get \frac{4}{3}.

$$\frac{\frac{81}{16}\times \frac{4}{3}}{\left(\frac{1}{3}\right)^{4}\left(-\frac{1}{2}\right)^{-4}\times \left(\frac{1}{9}\right)^{3}}$$

Multiply \frac{81}{16} and \frac{4}{3} to get \frac{27}{4}.

$$\frac{\frac{27}{4}}{\left(\frac{1}{3}\right)^{4}\left(-\frac{1}{2}\right)^{-4}\times \left(\frac{1}{9}\right)^{3}}$$

Calculate \frac{1}{3} to the power of 4 and get \frac{1}{81}.

$$\frac{\frac{27}{4}}{\frac{1}{81}\left(-\frac{1}{2}\right)^{-4}\times \left(\frac{1}{9}\right)^{3}}$$

Calculate -\frac{1}{2} to the power of -4 and get 16.

$$\frac{\frac{27}{4}}{\frac{1}{81}\times 16\times \left(\frac{1}{9}\right)^{3}}$$

Multiply \frac{1}{81} and 16 to get \frac{16}{81}.

$$\frac{\frac{27}{4}}{\frac{16}{81}\times \left(\frac{1}{9}\right)^{3}}$$

Calculate \frac{1}{9} to the power of 3 and get \frac{1}{729}.

$$\frac{\frac{27}{4}}{\frac{16}{81}\times \frac{1}{729}}$$

Multiply \frac{16}{81} and \frac{1}{729} to get \frac{16}{59049}.

$$\frac{\frac{27}{4}}{\frac{16}{59049}}$$

Divide \frac{27}{4} by \frac{16}{59049} by multiplying \frac{27}{4} by the reciprocal of \frac{16}{59049}.

$$\frac{27}{4}\times \frac{59049}{16}$$

Multiply \frac{27}{4} and \frac{59049}{16} to get \frac{1594323}{64}.

$$\frac{1594323}{64}$$

Factor

$$\frac{3 ^ {13}}{2 ^ {6}} = 24911\frac{19}{64} = 24911.296875$$