Answer: The answer is -1.
Step-by-step explanation: Given that 'a' and 'b' are integers such that their product is 5. We are to find the least possible value of 'a to the power b'.
Since a and b are integers and a × b = 5, so their possible values are
![a=1,~b=5,\\\\a=-1~b=-5,\\\\a=5,~b=1,\\\\a=-5,~b=-1.](https://img.qammunity.org/2020/formulas/mathematics/high-school/qm96yla5gef2ei280frrxqvb1p4ui1zhvi.png)
For these only four choices of a and b, we have the following values of a to the power b:
![a^b=1^5=1,\\\\a^b=(-1)^(-5)=(1)/((-1)^5)=(1)/(-1)=-1,\\\\\\a^b=5^1=5,\\\\a^b=(-5)^(-1)=(1)/((-5)^1)=-(1)/(5).](https://img.qammunity.org/2020/formulas/mathematics/high-school/g5gw46v2edll3e8trqhue7vz0ynj9238fl.png)
since -1 is the smallest among these four values, so the least possible value of 'a to the power b' is -1.
Thus, the answer is -1.