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
2.2 Given that a = -2, b = -3, c = 2 and d = 0, determine the value of the following expression: 2.2.1 (3abc)^d Step 1: Substitute the given values into the expression. (3 × (-2) × (-3) × 2)^0 Step 2: Calculate the value inside the parenthesis. (3 × 6 × 2)^0 (18 × 2)^0 (36)^0 Step 3: Apply the exponent rule x^0 = 1 for any non-zero x. = 1 1 2.2.2 a - 5b^2 + 4ac Step 1: Substitute the given values into the expression. -2 - 5(-3)^2 + 4(-2)(2) Step 2: Perform the exponentiation. -2 - 5(9) + 4(-2)(2) Step 3: Perform the multiplications. -2 - 45 + (-16) -2 - 45 - 16 Step 4: Perform the subtractions. -47 - 16 = -63 -63 2.2.3 36ab - 31bc + 2cd Step 1: Substitute the given values into the expression. 36(-2)(-3) - 31(-3)(2) + 2(2)(0) Step 2: Perform the multiplications in each term. 36(6) - 31(-6) + 0 216 - (-186) + 0 Step 3: Perform the addition. 216 + 186 = 402 402 2.2.4 (3)/(4)a^2 + (1)/(2)bc - (1)/(3)d Step 1: Substitute the given values into the expression. (3)/(4)(-2)^2 + (1)/(2)(-3)(2) - (1)/(3)(0) Step 2: Perform the exponentiation and multiplications. (3)/(4)(4) + (1)/(2)(-6) - 0 Step 3: Perform the remaining multiplications. 3 + (-3) - 0 Step 4: Perform the subtraction. 3 - 3 - 0 = 0 0 That's 2 down. 3 left today — send the next one.