Solve {l}{21/4+63/8}{08}{08^3/8}{08^5/8}{09}

$$\left. \begin{array} { l } { 21 / 4 + 63 / 8 } \\ { 08 } \\ { 08 ^ { 3 } / 8 } \\ { 08 ^ { 5 } / 8 } \\ { 09 } \end{array} \right.$$

Sort

$$8,9,\frac{105}{8},64,4096$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 3 to get 2.

$$sort(\frac{21}{4}+\frac{63}{8},8,8^{2},\frac{8^{5}}{8},9)$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 5 to get 4.

$$sort(\frac{21}{4}+\frac{63}{8},8,8^{2},8^{4},9)$$

Least common multiple of 4 and 8 is 8. Convert \frac{21}{4} and \frac{63}{8} to fractions with denominator 8.

$$sort(\frac{42}{8}+\frac{63}{8},8,8^{2},8^{4},9)$$

Since \frac{42}{8} and \frac{63}{8} have the same denominator, add them by adding their numerators.

$$sort(\frac{42+63}{8},8,8^{2},8^{4},9)$$

Add 42 and 63 to get 105.

$$sort(\frac{105}{8},8,8^{2},8^{4},9)$$

Calculate 8 to the power of 2 and get 64.

$$sort(\frac{105}{8},8,64,8^{4},9)$$

Calculate 8 to the power of 4 and get 4096.

$$sort(\frac{105}{8},8,64,4096,9)$$

Convert decimal numbers in the list \frac{105}{8},8,64,4096,9 to fractions.

$$\frac{105}{8},8,64,4096,9$$

To sort the list, start from a single element \frac{105}{8}.

$$\frac{105}{8}$$

Insert 8 to the appropriate location in the new list.

$$8,\frac{105}{8}$$

Insert 64 to the appropriate location in the new list.

$$8,\frac{105}{8},64$$

Insert 4096 to the appropriate location in the new list.

$$8,\frac{105}{8},64,4096$$

Insert 9 to the appropriate location in the new list.

$$8,9,\frac{105}{8},64,4096$$

Evaluate

$$\frac{105}{8},\ 8,\ 64,\ 4096,\ 9$$