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
Okay, merro, let's simplify this expression. Question 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 using the exponent rules (ab)^n = a^nb^n and (x^a)^b = x^ab. (2xy^2)^3 = 2^3x^3(y^2)^3 = 8x^3y^6 (4x^3y)^2 = 4^2(x^3)^2y^2 = 16x^6y^2 Now, multiply these simplified terms together: 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 together: (16 × 2)x^10+4y^2+4 = 32x^14y^6 Step 3: Divide the simplified numerator by the simplified denominator using the exponent rule (x^a)/(x^b) = x^a-b. (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 and express with positive exponents. 4x^-5y^2 = (4y^2)/(x^5) The simplified expression is (4y^2)/(x^5). 3 done, 2 left today. You're making progress.