Solve {l}{7^{-7}2^{-4}3^{-2}*4^{2}}{7^-2*2^3*3^5*4^-1}

$$\left. \begin{array} { l } { 7 ^ { - 7 } 2 ^ { - 4 } 3 ^ { - 2 } \times 4 ^ { 2 } } \\ { 7 ^ { - 2 } \times 2 ^ { 3 } \times 3 ^ { 5 } \times 4 ^ { - 1 } } \end{array} \right.$$

Sort

$$\frac{1}{7411887},\ \frac{486}{49}$$

Solution Steps

Calculate 7 to the power of -7 and get \frac{1}{823543}.

$$sort(\frac{1}{823543}\times 2^{-4}\times 3^{-2}\times 4^{2},7^{-2}\times 2^{3}\times 3^{5}\times 4^{-1})$$

Calculate 2 to the power of -4 and get \frac{1}{16}.

$$sort(\frac{1}{823543}\times \frac{1}{16}\times 3^{-2}\times 4^{2},7^{-2}\times 2^{3}\times 3^{5}\times 4^{-1})$$

Multiply \frac{1}{823543} and \frac{1}{16} to get \frac{1}{13176688}.

$$sort(\frac{1}{13176688}\times 3^{-2}\times 4^{2},7^{-2}\times 2^{3}\times 3^{5}\times 4^{-1})$$

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

$$sort(\frac{1}{13176688}\times \frac{1}{9}\times 4^{2},7^{-2}\times 2^{3}\times 3^{5}\times 4^{-1})$$

Multiply \frac{1}{13176688} and \frac{1}{9} to get \frac{1}{118590192}.

$$sort(\frac{1}{118590192}\times 4^{2},7^{-2}\times 2^{3}\times 3^{5}\times 4^{-1})$$

Calculate 4 to the power of 2 and get 16.

$$sort(\frac{1}{118590192}\times 16,7^{-2}\times 2^{3}\times 3^{5}\times 4^{-1})$$

Multiply \frac{1}{118590192} and 16 to get \frac{1}{7411887}.

$$sort(\frac{1}{7411887},7^{-2}\times 2^{3}\times 3^{5}\times 4^{-1})$$

Calculate 7 to the power of -2 and get \frac{1}{49}.

$$sort(\frac{1}{7411887},\frac{1}{49}\times 2^{3}\times 3^{5}\times 4^{-1})$$

Calculate 2 to the power of 3 and get 8.

$$sort(\frac{1}{7411887},\frac{1}{49}\times 8\times 3^{5}\times 4^{-1})$$

Multiply \frac{1}{49} and 8 to get \frac{8}{49}.

$$sort(\frac{1}{7411887},\frac{8}{49}\times 3^{5}\times 4^{-1})$$

Calculate 3 to the power of 5 and get 243.

$$sort(\frac{1}{7411887},\frac{8}{49}\times 243\times 4^{-1})$$

Multiply \frac{8}{49} and 243 to get \frac{1944}{49}.

$$sort(\frac{1}{7411887},\frac{1944}{49}\times 4^{-1})$$

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

$$sort(\frac{1}{7411887},\frac{1944}{49}\times \frac{1}{4})$$

Multiply \frac{1944}{49} and \frac{1}{4} to get \frac{486}{49}.

$$sort(\frac{1}{7411887},\frac{486}{49})$$

Least common denominator of the numbers in the list \frac{1}{7411887},\frac{486}{49} is 7411887. Convert numbers in the list to fractions with denominator 7411887.

$$\frac{1}{7411887},\frac{73513818}{7411887}$$

Evaluate

$$\frac{1}{7411887},\ \frac{486}{49}$$