Answer: When dividing terms with the same base, we subtract the exponents of the denominator from the exponents of the numerator.
So, for this expression:
(64x^10y) / (-14x^12y^4)
First, simplify the coefficients:
64 / (-14) = -64/14 = -32/7
Now, for the variable part, subtract the exponents of x and y:
x^10 / x^12 = x^(10-12) = x^(-2) = 1/x^2
y^1 / y^4 = y^(1-4) = y^(-3) = 1/y^3
Now, combine the simplified coefficients and the variables:
(-32/7) * (1/x^2) * (1/y^3) = -32/(7x^2y^3)
So, the simplified form of the expression is -32/(7x^2y^3).