Question

Find the quotient -44a^3b^4 - 64a^4b3 - 84ab ___________________ -4ab

Answer 1

When you divide a variable with an exponent by a variable with an exponent, you subtract the exponents (only if the bases/variables are the same)

For example:

$\frac{x^2}{y^2}$  Since they have different variables (x and y), you can't simplify this anymore

$\frac{x^5}{x^3} = x^{5-3}=x^2$

$\frac{z^3x^7}{z^2yx^2} = (\frac{1}{y})(z^{3-2})(x^{7-2}) = (\frac{1}{y} )(z^1)(x^5) = \frac{zx^5}{y}$

( if the exponent happens to come out negative, you have to move the variable and the exponent to the other side of the fraction to make the exponent positive)

Ex:

$\frac{x^2}{x^4} =x^{2-4}=x^{-2} = \frac{1}{x^2}$

$\frac{-44a^3b^4-64a^4b^3-84ab}{-4ab}$ SInce they all have a common factor of 4, you can divide out -4

$\frac{11a^3b^4+16a^4b^3+21ab}{ab}$

If you follow the steps from ^^^^^^^, you should get

$11a^2b^3+16a^3b^2+21$