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
[tex]a=1,~b=5,\\\\a=-1~b=-5,\\\\a=5,~b=1,\\\\a=-5,~b=-1.[/tex]
For these only four choices of a and b, we have the following values of a to the power b:
[tex]a^b=1^5=1,\\\\a^b=(-1)^{-5}=\dfrac{1}{(-1)^5}=\dfrac{1}{-1}=-1,\\\\\\a^b=5^1=5,\\\\a^b=(-5)^{-1}=\dfrac{1}{(-5)^1}=-\dfrac{1}{5}.[/tex]
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.
