Question

Marcus stated that any time an integer is raised to an integer exponent, the result is a rational number.

Is Marcus correct? Why or why not?
Select the option that is completely correct.
Marcus is incorrect. If any integer is raised to a negative integer exponent, the base is multiplied repeatedly. The product of two integers may not be a rational number.
Marcus is correct. If any integer is raised to any integer exponent, the base is multiplied or divided repeatedly. The product or quotient of integers is always a rational number.
Marcus is incorrect. If any integer is raised to a negative integer exponent, the base is divided repeatedly. The quotient of two integers may not be a rational number.
Marcus is correct. If any integer is raised to any integer exponent, the base is multiplied times the exponent. The product of two integers is always a rational number.

Answer 1

`(Integer)^(Integer)`

`2^3=2 * 2 * 2=8\\\\ 2^(-3)=(1)/(2)*(1)/(2)*(1)/(2)=(1)/(8), \\\\ (-2)^3=-2 * -2 * -2= -8,\\\\ (-2)^(-3)=(-1)/(2)*(-1)/(2)*(-1)/(2)=(-1)/(8),`

In all cases we are getting an integer.

So, yes, Marcus is correct.

Option D : Marcus is correct. If any integer is raised to any integer exponent, the base is multiplied times the exponent. The product of two integers is always a rational number.