How is 6p^5q^3 x 9p^5q^3 / 5p^5q^5= 30p^5q

because isn't it both have the same exponents and letters therefore they should cancel and be left with 30q^2

The equation started at as 25 for the second part of the numerator and not 9.
6p^5q^3 x 25p^5q^3/5p^5q^5 =
(150p^10q^6)/(5p^5q^5) =
30p^5q.

To simplify the expression (6p^5q^3 * 9p^5q^3) / (5p^5q^5), we can follow these steps:

Step 1: Multiply the numbers together.
6 * 9 = 54

Step 2: Multiply the variables with the same base together.
p^5 * p^5 = p^(5+5) = p^10
q^3 * q^3 = q^(3+3) = q^6

So far, we have (54p^10q^6) / (5p^5q^5).

Step 3: Divide the exponents.
p^10 / p^5 = p^(10-5) = p^5
q^6 / q^5 = q^(6-5) = q^1 = q

Now, the expression becomes (54p^5q) / (5q^5).

Step 4: Simplify the coefficients.
54 / 5 = 10 remainder 4. Therefore, the expression can be written as 10 + 4/5.

Finally, putting everything together, we get 10p^5q + 4p^5q / 5q^5. However, since the numerator and denominator have the same variable base, we can cancel out one "q" term from the numerator and denominator. This results in 10p^5q + 4p^5 / 5q^4.

In conclusion, the simplified expression is 10p^5q + 4p^5 / 5q^4, and not 30q^2 as you mentioned.