The problem is to simplify the expression $(p^5r^2)^4(-7p^3r)(6pr^3)$.

1. Problem Description

The problem is to simplify the expression $(p^5r^2)^4(-7p^3r)(6pr^3)$.

2. Solution Steps

First, we need to simplify $(p^5r^2)^4$ using the power of a power rule: $(a^m)^n = a^{m \cdot n}$.

$(p^5r^2)^4 = p^{5 \cdot 4}r^{2 \cdot 4} = p^{20}r^8$

Now, substitute this back into the original expression:

$p^{20}r^8(-7p^3r)(6pr^3)$

Next, we multiply the coefficients:

$-7 \cdot 6 = -42$

Now, we multiply the terms with $p$ using the rule $a^m \cdot a^n = a^{m+n}$:

$p^{20} \cdot p^3 \cdot p = p^{20+3+1} = p^{24}$

Similarly, we multiply the terms with $r$:

$r^8 \cdot r \cdot r^3 = r^{8+1+3} = r^{12}$

Combine all the terms together:

$-42p^{24}r^{12}$

3. Final Answer

$-42p^{24}r^{12}$