Simplify each of the following: a) 27^(2)/(3) x 9^(1)/(2) b) 25^-(3)/(2) x ((1)/(5))^-1 c) ((27)/(125))^-(2)/(3) x 81^(3)/(4)

Morning Omar — let's get this done. Here are the solutions for the visible questions: 4. Simplify each of the following a) 27^(2)/(3) × 9^(1)/(2) Step 1: Express the bases as powers of their prime factors. 27 = 3^3 9 = 3^2 Step 2: Substitute these into the expression. (3^3)^(2)/(3) × (3^2)^(1)/(2) Step 3: Apply the power rule (a^m)^n = a^mn. 3^3 × (2)/(3) × 3^2 × (1)/(2) 3^2 × 3^1 Step 4: Simplify the powers. 9 × 3 Step 5: Multiply the terms. 27 b) 25^-(3)/(2) × ((1)/(5))^-1 Step 1: Express the bases as powers of their prime factors. 25 = 5^2 (1)/(5) = 5^-1 Step 2: Substitute these into the expression. (5^2)^-(3)/(2) × (5^-1)^-1 Step 3: Apply the power rule (a^m)^n = a^mn. 5^2 × (-(3)/(2)) × 5^(-1) × (-1) 5^-3 × 5^1 Step 4: Apply the product rule a^m × a^n = a^m+n. 5^-3+1 5^-2 Step 5: Express with a positive exponent. (1)/(5^2) Step 6: Simplify the power. (1)/(25) c) ((27)/(125))^-(2)/(3) × 81^(3)/(4) Step 1: Express the bases as powers of their prime factors. (27)/(125) = (3^3)/(5^3) = ((3)/(5))^3 81 = 3^4 Step 2: Substitute these into the expression. (((3)/(5))^3)^-(2)/(3) × (3^4)^(3)/(4) Step 3: Apply the power rule (a^m)^n = a^mn. ((3)/(5))^3 × (-(2)/(3)) × 3^4 × (3)/(4) ((3)/(5))^-2 × 3^3 Step 4: Apply the negative exponent rule ((a)/(b))^-n = ((b)/(a))^n. ((5)/(3))^2 × 3^3 Step 5: Simplify the powers. (5^2)/(3^2) × 27 (25)/(9) × 27 Step 6: Multiply the terms. 25 × (27)/(9) 25 × 3 75 8. Solve each of the following equations a) x^2 + 6x + 8 = 0 Step 1: Factor the quadratic equation. We need two numbers that multiply to 8 (P) and add to 6 (S). These numbers are 4 and 2. x^2 + 4x + 2x + 8 = 0 Step 2: Group the terms and factor out common factors. x(x+4) + 2(x+4) = 0 Step 3: Factor out the common binomial (x+4). (x+2)(x+4) = 0 Step 4: Set each factor equal to zero and solve for x. x+2 = 0 or x+4 = 0 x = -2 or x = -4 x = -2, x = -4 Questions 3, 5(a), 5(b), 5(c), and 8(b) are incomplete in the image provided. Please send the full questions if you'd like me to solve them. Send me the next one 📸