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
Here is the solution for the 3rd question: 3. Find the product. 3 (i): (a^2) × (2a^22) × (4a^26) Step 1: Multiply the numerical coefficients and the variables separately. (1 × 2 × 4) × (a^2 × a^22 × a^26) Step 2: Multiply the coefficients and add the exponents of the variable a. 8 × a^(2+22+26) = 8a^50 3 (ii): ((2)/(3)xy) × (-(9)/(10)x^2y^2) Step 1: Multiply the numerical coefficients. ((2)/(3)) × (-(9)/(10)) Step 2: Multiply the variables by adding their exponents. x^(1+2)y^(1+2) Step 3: Simplify the product of the coefficients and combine with the variables. -(2 × 9)/(3 × 10)x^3y^3 = -(18)/(30)x^3y^3 Step 4: Reduce the fraction to its simplest form. = -(3)/(5)x^3y^3 3 (iii): (-(10)/(3)pq^3) × ((6)/(5)p^3q) Step 1: Multiply the numerical coefficients. (-(10)/(3)) × ((6)/(5)) Step 2: Multiply the variables by adding their exponents. p^(1+3)q^(3+1) Step 3: Simplify the product of the coefficients and combine with the variables. -(10 × 6)/(3 × 5)p^4q^4 = -(60)/(15)p^4q^4 Step 4: Reduce the fraction to its simplest form. = -4p^4q^4 3 (iv): x × x^2 × x^3 × x^4 Step 1: Add the exponents of the variable x. Remember that x is x^1. x^(1+2+3+4) Step 2: Perform the addition. = x^10 3 done, 2 left today. You're making progress.