Monomial expression multiplication (SAT). Game on.

Multiply the coefficients: $5 \cdot 3 = 15\textsf{.}$ Add the exponents on $x$: $x^{1+1} = x^{2}\textsf{.}$ So the product is $15x^{2}\textsf{.}$

Add exponents on matching variables: $a^{3+(-1)} b^{-4+2} = a^2 b^{-2}\textsf{.}$

Multiply the coefficients: $4 \cdot 2 = 8\textsf{.}$ Add the exponents on $a$: $a^{1+1} = a^{2}\textsf{.}$ The factor $b$ appears once, so the product is $8a^{2}b\textsf{.}$

Add exponents on matching variables: $p^{5+1} q^{2+4} r^{-3+2} = p^6 q^6 r^{-1}\textsf{.}$

Multiply the coefficients: $6 \cdot 1 \cdot 2 = 12\textsf{.}$ Add the exponents on $m$ and on $n$: $m^{1+1} n^{1+1} = m^{2} n^{2}\textsf{.}$ So the product is $12m^{2}n^{2}\textsf{.}$

Multiply the coefficients: $3 \cdot 4 = 12\textsf{.}$ Add the exponents on $x$: $x^{2+1} = x^{3}\textsf{.}$ So the product is $12x^{3}\textsf{.}$

Multiply the coefficients: $2 \cdot 5 \cdot 4 = 40\textsf{.}$ Add the exponents on $y$: $y^{1+1} = y^{2}\textsf{.}$ The factor $z$ appears once, so the product is $40y^{2}z\textsf{.}$

Multiply the coefficients: $7 \cdot 1 \cdot 2 = 14\textsf{.}$ Add the exponents on $p$ and on $q$: $p^{1+1} q^{1+1} = p^{2} q^{2}\textsf{.}$ So the product is $14p^{2}q^{2}\textsf{.}$