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.

[tex]2^3=2 \times 2 \times 2=8\\\\ 2^{-3}=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{8}, \\\\ (-2)^3=-2 \times -2 \times -2= -8,\\\\ (-2)^{-3}=\frac{-1}{2}\times\frac{-1}{2}\times\frac{-1}{2}=\frac{-1}{8},[/tex]

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.