This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You got it, merro! Let's finish these problems. Question 2 (continued) 2.3 Simplify (a^2b^3(a^3b)^2)/((a^-2)b^2)^-4. Step 1: Simplify the numerator using exponent rules (xy)^n = x^ny^n and x^a x^b = x^a+b. a^2b^3(a^3b)^2 = a^2b^3(a^3 × 2b^1 × 2) = a^2b^3(a^6b^2) = a^2+6b^3+2 = a^8b^5 Step 2: Simplify the denominator using exponent rules (xy)^n = x^ny^n and (x^a)^b = x^ab. (a^-2b^2)^-4 = a^(-2) × (-4)b^2 × (-4) = a^8b^-8 Step 3: Divide the simplified numerator by the simplified denominator using the rule (x^a)/(x^b) = x^a-b. (a^8b^5)/(a^8b^-8) = a^8-8b^5-(-8) = a^0b^5+8 = 1 · b^13 = b^13 The simplified expression is b^13. 2.4 Simplify ((2xy^2)^3 × (4x^3y)^2)/(4^2x^10)y^2 × 2x^4y^4. Step 1: Simplify the terms in the numerator. (2xy^2)^3 = 2^3x^3(y^2)^3 = 8x^3y^6 (4x^3y)^2 = 4^2(x^3)^2y^2 = 16x^6y^2 Multiply these simplified terms: 8x^3y^6 × 16x^6y^2 = (8 × 16)x^3+6y^6+2 = 128x^9y^8 Step 2: Simplify the terms in the denominator. 4^2x^10y^2 × 2x^4y^4 = 16x^10y^2 × 2x^4y^4 Multiply these terms: (16 × 2)x^10+4y^2+4 = 32x^14y^6 Step 3: Divide the simplified numerator by the simplified denominator. (128x^9y^8)/(32x^14)y^6 Divide the numerical coefficients: (128)/(32) = 4 Divide the x terms: (x^9)/(x^14) = x^9-14 = x^-5 Divide the y terms: (y^8)/(y^6) = y^8-6 = y^2 Step 4: Combine the simplified terms. 4x^-5y^2 = (4y^2)/(x^5) The simplified expression is (4y^2)/(x^5). That's 2 down. 3 left today — send the next one.