Question

Define two terms, each containing the variables x and y, with exponents on each. (For example: 10x'y-5) Find the quotient of the two terms. Explain step-by-step how you found the quotient.

Answer 1

We need to define two terms in the form:

$ax^by^c$

with a, b, and c constants. Then, we need to find the quotient of those terms.

One way to define those terms is by choosing the constants to be, for the first term:

$\begin{gathered} a=6 \\ b=3 \\ c=4 \end{gathered}$

Thus, the first term can be:

$6x^3y^4$

And. for the second term, we could choose, for instance:

$\begin{gathered} a=3 \\ b=2 \\ c=2 \end{gathered}$

Thus, the second term would be:

$3x^{2}y^{2}$

Now, the quotient of those terms can be found by grouping the terms with the same base and applying the rule:

$\frac{x^i}{x^j}=x^{i-j}$

Thus, we obtain:

$\frac{6x^3y^4}{3x^{2}y^{2}}=\frac{6}{3}\cdot\frac{x^3}{x^{2}}\cdot\frac{y^4}{y^{2}}=2\cdot x^{3-2}\cdot y^{4-2}=2x^{1}y^{2}=2xy^{2}$