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}{2^6*3^-2*3^3*2^6})}

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

Evaluate

$$\frac{7646540936605883684004049214900715851141976717930099881274424696364962224511494790223357992269746474039480563359188630818057376044379518831291702111276328210758059121435077756638722899626994299951506601517728490261014722259354212323631016519537502855612480246234345483953100325439456499764130713571240904682818279146104317908084764801177130893312}{243}\approx 3.146724665 \cdot 10^{343}$$

Solution Steps

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

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

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

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

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

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

Divide \frac{\frac{3^{3}\times 2^{2}}{3^{4}\times 2^{-2}\times 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{3^{4}\times 27\times 64}{2^{6\times 3^{1}\times 2^{6}}} by multiplying \frac{\frac{3^{3}\times 2^{2}}{3^{4}\times 2^{-2}\times 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{3^{4}\times 27\times 64}{2^{6\times 3^{1}\times 2^{6}}}.

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

Cancel out 3^{3} in both numerator and denominator.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

Calculate 2 to the power of 4 and get 16.

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

Calculate 4 to the power of 2 and get 16.

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

Multiply 3 and 16 to get 48.

$$\frac{\frac{16}{48}\times 2^{6\times 3^{1}\times 2^{6}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times 3^{4}\times 27\times 64}$$

Reduce the fraction \frac{16}{48} to lowest terms by extracting and canceling out 16.

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

Calculate 3 to the power of 1 and get 3.

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

Multiply 6 and 3 to get 18.

$$\frac{\frac{1}{3}\times 2^{18\times 2^{6}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times 3^{4}\times 27\times 64}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{\frac{1}{3}\times 2^{18\times 64}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times 3^{4}\times 27\times 64}$$

Multiply 18 and 64 to get 1152.

$$\frac{\frac{1}{3}\times 2^{1152}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times 3^{4}\times 27\times 64}$$

Calculate 2 to the power of 1152 and get 61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496.

$$\frac{\frac{1}{3}\times 61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times 3^{4}\times 27\times 64}$$

Multiply \frac{1}{3} and 61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496 to get \frac{61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496}{3}.

$$\frac{\frac{61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496}{3}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times 3^{4}\times 27\times 64}$$

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

$$\frac{\frac{61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496}{3}}{\frac{\frac{3}{4}\times \frac{4}{9}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times 3^{4}\times 27\times 64}$$

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

$$\frac{\frac{61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496}{3}}{\frac{\frac{1}{3}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times 3^{4}\times 27\times 64}$$

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

$$\frac{\frac{61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496}{3}}{\frac{\frac{1}{3}\times \frac{1}{3}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times 3^{4}\times 27\times 64}$$

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

$$\frac{\frac{61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496}{3}}{\frac{\frac{1}{9}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times 3^{4}\times 27\times 64}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\frac{61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496}{3}}{\frac{\frac{1}{9}}{\frac{9}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times 3^{4}\times 27\times 64}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\frac{61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496}{3}}{\frac{\frac{1}{9}}{\frac{9}{4}\times 4\times \frac{2^{3}}{3}}\times 3^{4}\times 27\times 64}$$

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

$$\frac{\frac{61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496}{3}}{\frac{\frac{1}{9}}{9\times \frac{2^{3}}{3}}\times 3^{4}\times 27\times 64}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\frac{61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496}{3}}{\frac{\frac{1}{9}}{9\times \frac{8}{3}}\times 3^{4}\times 27\times 64}$$

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

$$\frac{\frac{61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496}{3}}{\frac{\frac{1}{9}}{24}\times 3^{4}\times 27\times 64}$$

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

$$\frac{\frac{61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496}{3}}{\frac{1}{9\times 24}\times 3^{4}\times 27\times 64}$$

Multiply 9 and 24 to get 216.

$$\frac{\frac{61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496}{3}}{\frac{1}{216}\times 3^{4}\times 27\times 64}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{\frac{61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496}{3}}{\frac{1}{216}\times 81\times 27\times 64}$$

Multiply \frac{1}{216} and 81 to get \frac{3}{8}.

$$\frac{\frac{61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496}{3}}{\frac{3}{8}\times 27\times 64}$$

Multiply \frac{3}{8} and 27 to get \frac{81}{8}.

$$\frac{\frac{61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496}{3}}{\frac{81}{8}\times 64}$$

Multiply \frac{81}{8} and 64 to get 648.

$$\frac{\frac{61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496}{3}}{648}$$

Express \frac{\frac{61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496}{3}}{648} as a single fraction.

$$\frac{61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496}{3\times 648}$$

Multiply 3 and 648 to get 1944.

$$\frac{61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496}{1944}$$

Reduce the fraction \frac{61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496}{1944} to lowest terms by extracting and canceling out 8.

$$\frac{7646540936605883684004049214900715851141976717930099881274424696364962224511494790223357992269746474039480563359188630818057376044379518831291702111276328210758059121435077756638722899626994299951506601517728490261014722259354212323631016519537502855612480246234345483953100325439456499764130713571240904682818279146104317908084764801177130893312}{243}$$

Factor

$$\frac{2 ^ {1149}}{3 ^ {5}} = ∞\frac{NaN}{243} = ∞$$