Simplify the following algebraic expressions: 5d) 3/(2x3) - (8x2y)/(2y) 5f) sqrt((16x3y2)/(3y2)) + sqrt((96)/(2))

Alright Itu🩷🥹 — let's do this. Here are the solutions for questions 5d and 5f. 5d) Step 1: Simplify the terms inside the cube root and the fraction. 3/(2x^3) - (8x^2y)/(2y) Simplify the expression inside the cube root: (54x^3y^3)/(2x^3) = (54)/(2) · (x^3)/(x^3) · y^3 = 27y^3 Simplify the second fraction: (8x^2y)/(2y) = (8)/(2) · x^2 · (y)/(y) = 4x^2 Step 2: Evaluate the cube root. [3]27y^3 = [3]27 · [3]y^3 = 3y Step 3: Combine the simplified terms. 3y - 4x^2 The final answer is 3y - 4x^2. 5f) Step 1: Simplify the terms inside the square roots. sqrt((16x^3y^2)/(3y^2)) + sqrt((96)/(2)) Simplify the expression inside the first square root: (16x^3y^2)/(3y^2) = (16x^3)/(3) Simplify the expression inside the second square root: (96)/(2) = 48 Step 2: Simplify each square root. For the first term: sqrt((16x^3)/(3)) = sqrt(16x^3)sqrt(3) = sqrt(16x^2 · x)sqrt(3) = 4xsqrt(x)sqrt(3) Rationalize the denominator by multiplying the numerator and denominator by sqrt(3): 4xsqrt(x)sqrt(3) · sqrt(3)sqrt(3) = 4xsqrt(3x)3 For the second term: sqrt(48) = sqrt(16 · 3) = sqrt(16) · sqrt(3) = 4sqrt(3) Step 3: Combine the simplified terms. 4xsqrt(3x)3 + 4sqrt(3) The final answer is 4xsqrt(3x)3 + 4sqrt(3). Send me the next one 📸