Alright Mc — let's do this. Here are the solutions for simplifying the expressions: 1. $$ \frac{3p^{12}q^2 \times 10p^3q^5}{15pq^4} $$ Step 1: Multiply the terms in the numerator. 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 $30p^{15}q^7$. Step 2: Divide the simplified numerator by the denominator. $$ \frac{30p^{15}q^7}{15p^1q^4} $$ 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 $\frac{q^a}{q^b} = q^{a-b}$: $\frac{q^7}{q^4} = q^{7-4} = q^3$. Step 3: Combine the simplified terms. $$ 2p^{14}q^3 $$ The simplified expression is $\boxed{2p^{14}q^3}$. 2. $$ \frac{-5a^6y^4}{8a^4b^2} \times \frac{16a^3b^4}{10a^3b^3} $$ Step 1: Multiply the numerators and the denominators separately. 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 $80a^7b^5$. Step 2: Divide the combined numerator by the combined denominator. $$ \frac{-80a^9y^4b^4}{80a^7b^5} $$ 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: $\frac{b^4}{b^5} = b^{4-5} = b^{-1} = \frac{1}{b}$. Step 3: Combine the simplified terms. $$ -1 \times a^2 \times y^4 \times \frac{1}{b} = -\frac{a^2y^4}{b} $$ The simplified expression is $\boxed{-\frac{a^2y^4}{b}}$. Send me the next one 📸