(-12a^3b^5)/(4a^2b^7) state any restrictions on the variable(s) if they exist.

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Restrictions are that 'a' and 'b' cannot be zero. We could write and as shorthand.

The restrictions are put in place to ensure that you can't divide by zero.

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Explanation:

The coefficients -12 and 4 divide to -12/4 = -3 which is the coefficient for the answer in the numerator.

The 'a' terms divide to (a^3)/(a^2) = a^(3-2) = a^1 = a. We subtract the exponents to simplify.

The b terms are handled in a similar manner to get (b^5)/(b^7) = b^(5-7) = b^(-2) = 1/(b^2)

Putting all three results together has us end up with (-3a)/(b^2) where neither 'a' nor b are zero to prevent a division by zero error. We cannot have 0 in the denominator.

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