Solve frac{3^{2}:(2:3^3)^2}{2:(3:2^2)^-2}

$$\frac { 3 ^ { 2 } : ( 2 : 3 ^ { 3 } ) ^ { 2 } } { 2 : ( 3 : 2 ^ { 2 } ) ^ { - 2 } }$$

Evaluate

$$1458$$

Solution Steps

Divide \frac{3^{2}}{\left(\frac{2}{3^{3}}\right)^{2}} by \frac{2}{\left(\frac{3}{2^{2}}\right)^{-2}} by multiplying \frac{3^{2}}{\left(\frac{2}{3^{3}}\right)^{2}} by the reciprocal of \frac{2}{\left(\frac{3}{2^{2}}\right)^{-2}}.

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

Calculate 3 to the power of 2 and get 9.

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

Calculate 2 to the power of 2 and get 4.

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

Calculate \frac{3}{4} to the power of -2 and get \frac{16}{9}.

$$\frac{9\times \frac{16}{9}}{\left(\frac{2}{3^{3}}\right)^{2}\times 2}$$

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

$$\frac{16}{\left(\frac{2}{3^{3}}\right)^{2}\times 2}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{16}{\left(\frac{2}{27}\right)^{2}\times 2}$$

Calculate \frac{2}{27} to the power of 2 and get \frac{4}{729}.

$$\frac{16}{\frac{4}{729}\times 2}$$

Multiply \frac{4}{729} and 2 to get \frac{8}{729}.

$$\frac{16}{\frac{8}{729}}$$

Divide 16 by \frac{8}{729} by multiplying 16 by the reciprocal of \frac{8}{729}.

$$16\times \frac{729}{8}$$

Multiply 16 and \frac{729}{8} to get 1458.

$$1458$$

Factor

$$2\times 3^{6}$$