Solve {l}{4^{5}*8^{4}*16^-5}{(1/3)^3*3^-2*2^6}

$$\left. \begin{array} { l } { 4 ^ { 5 } \times 8 ^ { 4 } \times 16 ^ { - 5 } } \\ { ( \frac { 1 } { 3 } ) ^ { 3 } \times 3 ^ { - 2 } \times 2 ^ { 6 } } \end{array} \right.$$

Sort

$$\frac{64}{243},4$$

Solution Steps

Calculate 4 to the power of 5 and get 1024.

$$sort(1024\times 8^{4}\times 16^{-5},\left(\frac{1}{3}\right)^{3}\times 3^{-2}\times 2^{6})$$

Calculate 8 to the power of 4 and get 4096.

$$sort(1024\times 4096\times 16^{-5},\left(\frac{1}{3}\right)^{3}\times 3^{-2}\times 2^{6})$$

Multiply 1024 and 4096 to get 4194304.

$$sort(4194304\times 16^{-5},\left(\frac{1}{3}\right)^{3}\times 3^{-2}\times 2^{6})$$

Calculate 16 to the power of -5 and get \frac{1}{1048576}.

$$sort(4194304\times \frac{1}{1048576},\left(\frac{1}{3}\right)^{3}\times 3^{-2}\times 2^{6})$$

Multiply 4194304 and \frac{1}{1048576} to get 4.

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

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

$$sort(4,\frac{1}{27}\times 3^{-2}\times 2^{6})$$

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

$$sort(4,\frac{1}{27}\times \frac{1}{9}\times 2^{6})$$

Multiply \frac{1}{27} and \frac{1}{9} to get \frac{1}{243}.

$$sort(4,\frac{1}{243}\times 2^{6})$$

Calculate 2 to the power of 6 and get 64.

$$sort(4,\frac{1}{243}\times 64)$$

Multiply \frac{1}{243} and 64 to get \frac{64}{243}.

$$sort(4,\frac{64}{243})$$

Convert decimal numbers in the list 4,\frac{64}{243} to fractions.

$$4,\frac{64}{243}$$

To sort the list, start from a single element 4.

$$4$$

Insert \frac{64}{243} to the appropriate location in the new list.

$$\frac{64}{243},4$$

Evaluate

$$4,\ \frac{64}{243}$$