3p12q2 x 10p3q515pq4

Alright Mc — let's do this. Here are the solutions for simplifying the expressions: 1. 3p^12q^2 × 10p^3q^515pq^4 Step 1: Multiply the terms in the numerator. Multiply the coefficients: 3 × 10 = 30. Combine the p terms using p^a × p^b = p^a+b: p^12 × p^3 = p^12+3 = p^15. Combine the q terms using q^a × q^b = q^a+b: q^2 × q^5 = q^2+5 = q^7. The numerator becomes 30p^15q^7. Step 2: Divide the simplified numerator by the denominator. 30p^15q^715p^1q^4 Divide the coefficients: (30)/(15) = 2. Divide the p terms using (p^a)/(p^b) = p^a-b: p^15p^1 = p^15-1 = p^14. Divide the q terms using (q^a)/(q^b) = q^a-b: (q^7)/(q^4) = q^7-4 = q^3. Step 3: Combine the simplified terms. 2p^14q^3 The simplified expression is 2p^14q^3. 2. (-5a^6y^4)/(8a^4b^2) × (16a^3b^4)/(10a^3b^3) Step 1: Multiply the numerators and the denominators separately. Numerator: (-5a^6y^4) × (16a^3b^4) Multiply coefficients: -5 × 16 = -80. Combine a terms: a^6 × 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) × (10a^3b^3) Multiply coefficients: 8 × 10 = 80. Combine a terms: a^4 × a^3 = a^4+3 = a^7. Combine b terms: b^2 × 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. (-80a^9y^4b^4)/(80a^7b^5) Divide the coefficients: (-80)/(80) = -1. Divide the a terms: (a^9)/(a^7) = a^9-7 = a^2. The y^4 term remains in the numerator. Divide the b terms: (b^4)/(b^5) = b^4-5 = b^-1 = (1)/(b). Step 3: Combine the simplified terms. -1 × a^2 × y^4 × (1)/(b) = -(a^2y^4)/(b) The simplified expression is -(a^2y^4)/(b). Send me the next one 📸