Solve {l}{125^125:125^124}{[(-1)^9:(1)^2]}

$$\left. \begin{array} { l } { 125 ^ { 125 } : 125 ^ { 124 } } \\ { [ ( - 1 ) ^ { 9 } : ( 1 ) ^ { 2 } ] } \end{array} \right.$$

Sort

$$-1,125$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 124 from 125 to get 1.

$$sort(125^{1},\frac{\left(-1\right)^{9}}{1^{2}})$$

Calculate 125 to the power of 1 and get 125.

$$sort(125,\frac{\left(-1\right)^{9}}{1^{2}})$$

Calculate -1 to the power of 9 and get -1.

$$sort(125,\frac{-1}{1^{2}})$$

Calculate 1 to the power of 2 and get 1.

$$sort(125,\frac{-1}{1})$$

Anything divided by one gives itself.

$$sort(125,-1)$$

To sort the list, start from a single element 125.

$$125$$

Insert -1 to the appropriate location in the new list.

$$-1,125$$

Evaluate

$$125,\ -1$$