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
1. Evaluate ((27)/(64))^(1)/(3) Step 1: Apply the fractional exponent to both the numerator and the denominator. A power of (1)/(3) is equivalent to taking the cube root. ((27)/(64))^(1)/(3) = (27^1)/(3)64^(1)/(3) = [3]27[3]64 Step 2: Calculate the cube root of the numerator and the denominator. [3]27 = 3 because 3 × 3 × 3 = 27 [3]64 = 4 because 4 × 4 × 4 = 64 Step 3: Substitute the cube roots back into the fraction. [3]27[3]64 = (3)/(4) The evaluated expression is: (3)/(4) 2. Factorise completely pq - 3p - q^2 + 3q. Step 1: Group the terms to look for common factors. (pq - 3p) + (-q^2 + 3q) Step 2: Factor out the common factor from each group. From the first group, factor out p: p(q - 3) From the second group, factor out -q: -q(q - 3) The expression now is: p(q - 3) - q(q - 3) Step 3: Factor out the common binomial factor (q - 3). (q - 3)(p - q) The completely factorised expression is: (q - 3)(p - q) 3. Simplify 8x + 4 - 3(2x - 3). Step 1: Distribute the -3 into the parenthesis. 8x + 4 - 3(2x) - 3(-3) 8x + 4 - 6x + 9 Step 2: Combine the like terms. Combine the x terms: 8x - 6x = 2x Combine the constant terms: 4 + 9 = 13 Step 3: Write the simplified expression. 2x + 13 The simplified expression is: 2x + 13 Send me the next one 📸