Solve {l}{frac{5^{11}}{3^-4}}{2^-7*3^5/7^8}

$$\left. \begin{array} { l } { \frac { 5 ^ { 11 } } { 3 ^ { - 4 } } } \\ { 2 ^ { - 7 } \times \frac { 3 ^ { 5 } } { 7 ^ { 8 } } } \end{array} \right.$$

Sort

$$\frac{243}{737894528},3955078125$$

Solution Steps

Calculate 5 to the power of 11 and get 48828125.

$$sort(\frac{48828125}{3^{-4}},2^{-7}\times \frac{3^{5}}{7^{8}})$$

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

$$sort(\frac{48828125}{\frac{1}{81}},2^{-7}\times \frac{3^{5}}{7^{8}})$$

Divide 48828125 by \frac{1}{81} by multiplying 48828125 by the reciprocal of \frac{1}{81}.

$$sort(48828125\times 81,2^{-7}\times \frac{3^{5}}{7^{8}})$$

Multiply 48828125 and 81 to get 3955078125.

$$sort(3955078125,2^{-7}\times \frac{3^{5}}{7^{8}})$$

Calculate 2 to the power of -7 and get \frac{1}{128}.

$$sort(3955078125,\frac{1}{128}\times \frac{3^{5}}{7^{8}})$$

Calculate 3 to the power of 5 and get 243.

$$sort(3955078125,\frac{1}{128}\times \frac{243}{7^{8}})$$

Calculate 7 to the power of 8 and get 5764801.

$$sort(3955078125,\frac{1}{128}\times \frac{243}{5764801})$$

Multiply \frac{1}{128} and \frac{243}{5764801} to get \frac{243}{737894528}.

$$sort(3955078125,\frac{243}{737894528})$$

Convert decimal numbers in the list 3955078125,\frac{243}{737894528} to fractions.

$$3955078125,\frac{243}{737894528}$$

To sort the list, start from a single element 3955078125.

$$3955078125$$

Insert \frac{243}{737894528} to the appropriate location in the new list.

$$\frac{243}{737894528},3955078125$$

Evaluate

$$3955078125,\ \frac{243}{737894528}$$