3p^(12q² x 10p³q⁵)15pq⁴

Multiply the coefficients: $3 \times 10 = 30$.
Combine the $p$ terms using $p^a \times p^b = p^{a+b}$: $p^{12} \times p^3 = p^{12+3} = p^{15}$.
Combine the $q$ terms using $q^a \times q^b = q^{a+b}$: $q^2 \times q^5 = q^{2+5} = q^7$.
The numerator becomes $30p^{15}q^7$.

Divide the coefficients: $\frac{30}{15} = 2$.
Divide the $p$ terms using $\frac{p^a}{p^b} = p^{a-b}$: $\frac{p^{15}}{p^1} = p^{15-1} = p^{14}$.
Divide the $q$ terms using $\frac{q^a}{q^b} = q^{a-b}$: $\frac{q^7}{q^4} = q^{7-4} = q^3$.

The simplified expression is $\boxed{2p^{14}q^3}$.

2.

Numerator: $(-5a^6y^4) \times (16a^3b^4)$
Multiply coefficients: $-5 \times 16 = -80$.
Combine $a$ terms: $a^6 \times a^3 = a^{6+3} = a^9$.
The $y^4$ and $b^4$ terms remain as they are.
So, the combined numerator is $-80a^9y^4b^4$.

Denominator: $(8a^4b^2) \times (10a^3b^3)$
Multiply coefficients: $8 \times 10 = 80$.
Combine $a$ terms: $a^4 \times a^3 = a^{4+3} = a^7$.
Combine $b$ terms: $b^2 \times b^3 = b^{2+3} = b^5$.
So, the combined denominator is $80a^7b^5$.

Divide the coefficients: $\frac{-80}{80} = -1$.
Divide the $a$ terms: $\frac{a^9}{a^7} = a^{9-7} = a^2$.
The $y^4$ term remains in the numerator.
Divide the $b$ terms: $\frac{b^4}{b^5} = b^{4-5} = b^{-1} = \frac{1}{b}$.

The simplified expression is $\boxed{-\frac{a^2y^4}{b}}$.