Solve (6^-2*12^3*20^2/10^4*{18^3})*({5}^-2*{3}^-3*{2}^-3)

$$( \frac{ { 6 }^{ -2 } \times { 12 }^{ 3 } \times { 20 }^{ 2 } }{ { 10 }^{ 4 } \times { 18 }^{ 3 } } ) \times ( { 5 }^{ -2 } \times { 3 }^{ -3 } \times { 2 }^{ -3 } )$$

Evaluate

$$\frac{1}{16402500}\approx 0.000000061$$

Solution Steps

Calculate 6 to the power of -2 and get \frac{1}{36}.

$$\frac{\frac{1}{36}\times 12^{3}\times 20^{2}}{10^{4}\times 18^{3}}\times 5^{-2}\times 3^{-3}\times 2^{-3}$$

Calculate 12 to the power of 3 and get 1728.

$$\frac{\frac{1}{36}\times 1728\times 20^{2}}{10^{4}\times 18^{3}}\times 5^{-2}\times 3^{-3}\times 2^{-3}$$

Multiply \frac{1}{36} and 1728 to get 48.

$$\frac{48\times 20^{2}}{10^{4}\times 18^{3}}\times 5^{-2}\times 3^{-3}\times 2^{-3}$$

Calculate 20 to the power of 2 and get 400.

$$\frac{48\times 400}{10^{4}\times 18^{3}}\times 5^{-2}\times 3^{-3}\times 2^{-3}$$

Multiply 48 and 400 to get 19200.

$$\frac{19200}{10^{4}\times 18^{3}}\times 5^{-2}\times 3^{-3}\times 2^{-3}$$

Calculate 10 to the power of 4 and get 10000.

$$\frac{19200}{10000\times 18^{3}}\times 5^{-2}\times 3^{-3}\times 2^{-3}$$

Calculate 18 to the power of 3 and get 5832.

$$\frac{19200}{10000\times 5832}\times 5^{-2}\times 3^{-3}\times 2^{-3}$$

Multiply 10000 and 5832 to get 58320000.

$$\frac{19200}{58320000}\times 5^{-2}\times 3^{-3}\times 2^{-3}$$

Reduce the fraction \frac{19200}{58320000} to lowest terms by extracting and canceling out 9600.

$$\frac{2}{6075}\times 5^{-2}\times 3^{-3}\times 2^{-3}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{2}{6075}\times \frac{1}{25}\times 3^{-3}\times 2^{-3}$$

Multiply \frac{2}{6075} and \frac{1}{25} to get \frac{2}{151875}.

$$\frac{2}{151875}\times 3^{-3}\times 2^{-3}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{2}{151875}\times \frac{1}{27}\times 2^{-3}$$

Multiply \frac{2}{151875} and \frac{1}{27} to get \frac{2}{4100625}.

$$\frac{2}{4100625}\times 2^{-3}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{2}{4100625}\times \frac{1}{8}$$

Multiply \frac{2}{4100625} and \frac{1}{8} to get \frac{1}{16402500}.

$$\frac{1}{16402500}$$

Factor

$$\frac{1}{2 ^ {2} \cdot 3 ^ {8} \cdot 5 ^ {4}} = 6.096631611034903 \times 10^{-8}$$