When you divide powers with the same base, use $\frac{a^m}{a^n} = a^{m-n}$. Apply this separately for the $x$ terms and the $y$ terms.

After you subtract the exponents, you will get a negative exponent for $y$. Remember $a^{-n} = \frac{1}{a^n}$, so think about whether that factor belongs in the numerator or denominator in the final answer.

In Desmos, define two positive numbers, for example by typing x=2 and y=3. Then type the original expression (12*x^9*y^-4)/(3*x^-2*y^5) and note the numerical value that Desmos shows.

Using the same values of x and y, type each choice’s expression (A, B, C, and D) into Desmos, one per line. Compare the numerical value of each choice with the value of the original expression; any choice that does not match can be eliminated.

To be extra sure, change to another pair of positive values, such as x=5 and y=2, and again compare the numerical value of the original expression with each answer choice. The expression that matches the original both times is the correct option.

Rewrite the fraction by separating the number part and each variable part:

Now first simplify the numerical fraction $\frac{12}{3}$ to get $4$.

Use the rule for dividing powers with the same base: $\frac{a^m}{a^n} = a^{m-n}$.

For the $x$ terms:

So far, the expression becomes $4\cdot x^{11}\cdot\frac{y^{-4}}{y^{5}}$.

Use the same rule for the $y$ terms:

Now the expression is $4x^{11}y^{-9}$.

Recall that a negative exponent means a reciprocal: $a^{-n} = \frac{1}{a^n}$.

So $y^{-9} = \frac{1}{y^9}$, and

Therefore, the equivalent expression is $\dfrac{4x^{11}}{y^{9}}$.