If pq = 3, then p^3q^4 + p^4q^5 =

A. 12q
B. 7p + 9q
C. 12p + 20q
D. 96p
E. 108q

(p q)^3 ( q + p q^2)

3^3 ( q + 3 q)

3^3 (4q)

27 (4 q)

108 q

Thank you so much, Damon.

To solve this problem, we need to use the given equation pq = 3 and substitute it into the expression p^3q^4 + p^4q^5. Let's break it down step by step:

First, substitute the value of pq in the expression: (3)^3(3)^4 + (3)^4(3)^5

Next, simplify the exponents: 3^3 = 27, 3^4 = 81, and 3^5 = 243. Substitute these values into the expression: 27(81) + 81(243)

Now, perform the multiplication: 2187 + 19683

Finally, add the two values together: 2187 + 19683 = 21870

So the value of p^3q^4 + p^4q^5 is 21,870.

However, none of the answer choices match the result obtained. Hence, none of the given options are correct.