Solve {l}{(8^{-3})^{2}*8^{2}*8}{9^-2*(9^-4)^2*9^5}

$$\left. \begin{array} { l } { ( 8 ^ { - 3 } ) ^ { 2 } \times 8 ^ { 2 } \times 8 } \\ { 9 ^ { - 2 } \times ( 9 ^ { - 4 } ) ^ { 2 } \times 9 ^ { 5 } } \end{array} \right.$$

Sort

$$\frac{1}{59049},\frac{1}{512}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -3 and 2 to get -6.

$$sort(8^{-6}\times 8^{2}\times 8,9^{-2}\times \left(9^{-4}\right)^{2}\times 9^{5})$$

To multiply powers of the same base, add their exponents. Add -6 and 2 to get -4.

$$sort(8^{-4}\times 8,9^{-2}\times \left(9^{-4}\right)^{2}\times 9^{5})$$

To multiply powers of the same base, add their exponents. Add -4 and 1 to get -3.

$$sort(8^{-3},9^{-2}\times \left(9^{-4}\right)^{2}\times 9^{5})$$

To raise a power to another power, multiply the exponents. Multiply -4 and 2 to get -8.

$$sort(8^{-3},9^{-2}\times 9^{-8}\times 9^{5})$$

To multiply powers of the same base, add their exponents. Add -2 and -8 to get -10.

$$sort(8^{-3},9^{-10}\times 9^{5})$$

To multiply powers of the same base, add their exponents. Add -10 and 5 to get -5.

$$sort(8^{-3},9^{-5})$$

Calculate 8 to the power of -3 and get \frac{1}{512}.

$$sort(\frac{1}{512},9^{-5})$$

Calculate 9 to the power of -5 and get \frac{1}{59049}.

$$sort(\frac{1}{512},\frac{1}{59049})$$

Least common denominator of the numbers in the list \frac{1}{512},\frac{1}{59049} is 30233088. Convert numbers in the list to fractions with denominator 30233088.

$$\frac{59049}{30233088},\frac{512}{30233088}$$

To sort the list, start from a single element \frac{59049}{30233088}.

$$\frac{59049}{30233088}$$

Insert \frac{512}{30233088} to the appropriate location in the new list.

$$\frac{512}{30233088},\frac{59049}{30233088}$$

Replace the obtained fractions with the initial values.

$$\frac{1}{59049},\frac{1}{512}$$

Evaluate

$$\frac{1}{512},\ \frac{1}{59049}$$