Solve {l}{(2^3)}{(3^-7div3^-10)*3^-5}

$$\left. \begin{array} { l } { ( 2 ^ { 3 } ) } \\ { ( 3 ^ { - 7 } \div 3 ^ { - 10 } ) \times 3 ^ { - 5 } } \end{array} \right.$$

Sort

$$\frac{1}{9},8$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -10 from -7 to get 3.

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

To multiply powers of the same base, add their exponents. Add 3 and -5 to get -2.

$$sort(2^{3},3^{-2})$$

Calculate 2 to the power of 3 and get 8.

$$sort(8,3^{-2})$$

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

$$sort(8,\frac{1}{9})$$

Convert decimal numbers in the list 8,\frac{1}{9} to fractions.

$$8,\frac{1}{9}$$

To sort the list, start from a single element 8.

$$8$$

Insert \frac{1}{9} to the appropriate location in the new list.

$$\frac{1}{9},8$$

Evaluate

$$8,\ \frac{1}{9}$$