Solve frac{(frac{3^{7}*3^{-4}*2^{2}}{3^{4}*2^{-2}-4^{2}})div(3/4(frac{2/3)^{2}2/6}{frac{3^{2}}{4}*frac{2^{3}}{2}*frac{2^{3}}{3}})}{(frac{3^{4}-27-64}{2^{4}*2*2^{3}})div(frac{4-16*27*3^{-2}}{2^6+3^-2*3^3*2^6})}

$$\frac { ( \frac { 3 ^ { 7 } \cdot 3 ^ { - 4 } \cdot 2 ^ { 2 } } { 3 ^ { 4 } \cdot 2 ^ { - 2 } - 4 ^ { 2 } } ) \div ( \frac { \frac { 3 } { 4 } ( \frac { 2 } { 3 } ) ^ { 2 } \frac { 2 } { 6 } } { \frac { 3 ^ { 2 } } { 4 } \cdot \frac { 2 ^ { 3 } } { 2 } \cdot \frac { 2 ^ { 3 } } { 3 } } ) } { ( \frac { 3 ^ { 4 } - 27 - 64 } { 2 ^ { 4 } \cdot 2 \cdot 2 ^ { 3 } } ) \div ( \frac { 4 - 16 \cdot 27 \cdot 3 ^ { - 2 } } { 2 ^ { 6 } + 3 ^ { - 2 } \cdot 3 ^ { 3 } \cdot 2 ^ { 6 } } ) }$$

Evaluate

$$\frac{2052864}{85}\approx 24151.341176471$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and -4 to get 3.

$$\frac{\frac{\frac{3^{3}\times 2^{2}}{3^{4}\times 2^{-2}-4^{2}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times \frac{2^{3}}{2}\times \frac{2^{3}}{3}}}}{\frac{\frac{3^{4}-27-64}{2^{4}\times 2\times 2^{3}}}{\frac{4-16\times 27\times 3^{-2}}{2^{6}+3^{-2}\times 3^{3}\times 2^{6}}}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 3 to get 2.

$$\frac{\frac{\frac{3^{3}\times 2^{2}}{3^{4}\times 2^{-2}-4^{2}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}}}{\frac{\frac{3^{4}-27-64}{2^{4}\times 2\times 2^{3}}}{\frac{4-16\times 27\times 3^{-2}}{2^{6}+3^{-2}\times 3^{3}\times 2^{6}}}}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{\frac{\frac{3^{3}\times 2^{2}}{3^{4}\times 2^{-2}-4^{2}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}}}{\frac{\frac{3^{4}-27-64}{2^{5}\times 2^{3}}}{\frac{4-16\times 27\times 3^{-2}}{2^{6}+3^{-2}\times 3^{3}\times 2^{6}}}}$$

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$\frac{\frac{\frac{3^{3}\times 2^{2}}{3^{4}\times 2^{-2}-4^{2}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}}}{\frac{\frac{3^{4}-27-64}{2^{8}}}{\frac{4-16\times 27\times 3^{-2}}{2^{6}+3^{-2}\times 3^{3}\times 2^{6}}}}$$

To multiply powers of the same base, add their exponents. Add -2 and 3 to get 1.

$$\frac{\frac{\frac{3^{3}\times 2^{2}}{3^{4}\times 2^{-2}-4^{2}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}}}{\frac{\frac{3^{4}-27-64}{2^{8}}}{\frac{4-16\times 27\times 3^{-2}}{2^{6}+3^{1}\times 2^{6}}}}$$

Divide \frac{\frac{3^{3}\times 2^{2}}{3^{4}\times 2^{-2}-4^{2}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}} by \frac{\frac{3^{4}-27-64}{2^{8}}}{\frac{4-16\times 27\times 3^{-2}}{2^{6}+3^{1}\times 2^{6}}} by multiplying \frac{\frac{3^{3}\times 2^{2}}{3^{4}\times 2^{-2}-4^{2}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}} by the reciprocal of \frac{\frac{3^{4}-27-64}{2^{8}}}{\frac{4-16\times 27\times 3^{-2}}{2^{6}+3^{1}\times 2^{6}}}.

$$\frac{\frac{3^{3}\times 2^{2}}{3^{4}\times 2^{-2}-4^{2}}\times \frac{4-16\times 27\times 3^{-2}}{2^{6}+3^{1}\times 2^{6}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{\frac{27\times 2^{2}}{3^{4}\times 2^{-2}-4^{2}}\times \frac{4-16\times 27\times 3^{-2}}{2^{6}+3^{1}\times 2^{6}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\frac{27\times 4}{3^{4}\times 2^{-2}-4^{2}}\times \frac{4-16\times 27\times 3^{-2}}{2^{6}+3^{1}\times 2^{6}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Multiply 27 and 4 to get 108.

$$\frac{\frac{108}{3^{4}\times 2^{-2}-4^{2}}\times \frac{4-16\times 27\times 3^{-2}}{2^{6}+3^{1}\times 2^{6}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{\frac{108}{81\times 2^{-2}-4^{2}}\times \frac{4-16\times 27\times 3^{-2}}{2^{6}+3^{1}\times 2^{6}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

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

$$\frac{\frac{108}{81\times \frac{1}{4}-4^{2}}\times \frac{4-16\times 27\times 3^{-2}}{2^{6}+3^{1}\times 2^{6}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Multiply 81 and \frac{1}{4} to get \frac{81}{4}.

$$\frac{\frac{108}{\frac{81}{4}-4^{2}}\times \frac{4-16\times 27\times 3^{-2}}{2^{6}+3^{1}\times 2^{6}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{\frac{108}{\frac{81}{4}-16}\times \frac{4-16\times 27\times 3^{-2}}{2^{6}+3^{1}\times 2^{6}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Subtract 16 from \frac{81}{4} to get \frac{17}{4}.

$$\frac{\frac{108}{\frac{17}{4}}\times \frac{4-16\times 27\times 3^{-2}}{2^{6}+3^{1}\times 2^{6}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Divide 108 by \frac{17}{4} by multiplying 108 by the reciprocal of \frac{17}{4}.

$$\frac{108\times \frac{4}{17}\times \frac{4-16\times 27\times 3^{-2}}{2^{6}+3^{1}\times 2^{6}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Multiply 108 and \frac{4}{17} to get \frac{432}{17}.

$$\frac{\frac{432}{17}\times \frac{4-16\times 27\times 3^{-2}}{2^{6}+3^{1}\times 2^{6}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Multiply 16 and 27 to get 432.

$$\frac{\frac{432}{17}\times \frac{4-432\times 3^{-2}}{2^{6}+3^{1}\times 2^{6}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{432}{17}\times \frac{4-432\times \frac{1}{9}}{2^{6}+3^{1}\times 2^{6}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Multiply 432 and \frac{1}{9} to get 48.

$$\frac{\frac{432}{17}\times \frac{4-48}{2^{6}+3^{1}\times 2^{6}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Subtract 48 from 4 to get -44.

$$\frac{\frac{432}{17}\times \frac{-44}{2^{6}+3^{1}\times 2^{6}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{\frac{432}{17}\times \frac{-44}{64+3^{1}\times 2^{6}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Calculate 3 to the power of 1 and get 3.

$$\frac{\frac{432}{17}\times \frac{-44}{64+3\times 2^{6}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{\frac{432}{17}\times \frac{-44}{64+3\times 64}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Multiply 3 and 64 to get 192.

$$\frac{\frac{432}{17}\times \frac{-44}{64+192}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Add 64 and 192 to get 256.

$$\frac{\frac{432}{17}\times \frac{-44}{256}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Reduce the fraction \frac{-44}{256} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{432}{17}\left(-\frac{11}{64}\right)}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Multiply \frac{432}{17} and -\frac{11}{64} to get -\frac{297}{68}.

$$\frac{-\frac{297}{68}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

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

$$\frac{-\frac{297}{68}}{\frac{\frac{3}{4}\times \frac{4}{9}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Multiply \frac{3}{4} and \frac{4}{9} to get \frac{1}{3}.

$$\frac{-\frac{297}{68}}{\frac{\frac{1}{3}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{297}{68}}{\frac{\frac{1}{3}\times \frac{1}{3}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Multiply \frac{1}{3} and \frac{1}{3} to get \frac{1}{9}.

$$\frac{-\frac{297}{68}}{\frac{\frac{1}{9}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{-\frac{297}{68}}{\frac{\frac{1}{9}}{\frac{9}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{-\frac{297}{68}}{\frac{\frac{1}{9}}{\frac{9}{4}\times 4\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

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

$$\frac{-\frac{297}{68}}{\frac{\frac{1}{9}}{9\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{-\frac{297}{68}}{\frac{\frac{1}{9}}{9\times \frac{8}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Multiply 9 and \frac{8}{3} to get 24.

$$\frac{-\frac{297}{68}}{\frac{\frac{1}{9}}{24}\times \frac{3^{4}-27-64}{2^{8}}}$$

Express \frac{\frac{1}{9}}{24} as a single fraction.

$$\frac{-\frac{297}{68}}{\frac{1}{9\times 24}\times \frac{3^{4}-27-64}{2^{8}}}$$

Multiply 9 and 24 to get 216.

$$\frac{-\frac{297}{68}}{\frac{1}{216}\times \frac{3^{4}-27-64}{2^{8}}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{-\frac{297}{68}}{\frac{1}{216}\times \frac{81-27-64}{2^{8}}}$$

Subtract 27 from 81 to get 54.

$$\frac{-\frac{297}{68}}{\frac{1}{216}\times \frac{54-64}{2^{8}}}$$

Subtract 64 from 54 to get -10.

$$\frac{-\frac{297}{68}}{\frac{1}{216}\times \frac{-10}{2^{8}}}$$

Calculate 2 to the power of 8 and get 256.

$$\frac{-\frac{297}{68}}{\frac{1}{216}\times \frac{-10}{256}}$$

Reduce the fraction \frac{-10}{256} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{297}{68}}{\frac{1}{216}\left(-\frac{5}{128}\right)}$$

Multiply \frac{1}{216} and -\frac{5}{128} to get -\frac{5}{27648}.

$$\frac{-\frac{297}{68}}{-\frac{5}{27648}}$$

Divide -\frac{297}{68} by -\frac{5}{27648} by multiplying -\frac{297}{68} by the reciprocal of -\frac{5}{27648}.

$$-\frac{297}{68}\left(-\frac{27648}{5}\right)$$

Multiply -\frac{297}{68} and -\frac{27648}{5} to get \frac{2052864}{85}.

$$\frac{2052864}{85}$$

Factor

$$\frac{2 ^ {8} \cdot 3 ^ {6} \cdot 11}{5 \cdot 17} = 24151\frac{29}{85} = 24151.34117647059$$