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
Okay, Itu🩷🥹, I understand. My apologies for any confusion. Let's focus on questions 5d and 5f from the image, keeping it simple and clear. Here are the solutions for 5d and 5f, based on the image you sent. 5d) The expression is: 3/(2x^3) - sqrt((8x^2y^3)/(2y)) Step 1: Simplify the fractions inside each root. For the first part: (54x^6y^3)/(2x^3) = (54 ÷ 2) · (x^6 ÷ x^3) · y^3 = 27x^6-3y^3 = 27x^3y^3 For the second part: (8x^2y^3)/(2y) = (8 ÷ 2) · x^2 · (y^3 ÷ y) = 4x^2y^3-1 = 4x^2y^2 Now the expression is: [3]27x^3y^3 - sqrt(4x^2y^2) Step 2: Take the cube root and the square root. For the first term, [3]27x^3y^3: [3]27 · [3]x^3 · [3]y^3 = 3 · x · y = 3xy For the second term, sqrt(4x^2y^2): sqrt(4) · sqrt(x^2) · sqrt(y^2) = 2 · x · y = 2xy Step 3: Combine the simplified terms. 3xy - 2xy = xy The final answer is xy. 5f) The expression is: 3/(2x^3) - sqrt((32y^8)/(9y^2)) + sqrt((98y^6)/(2)) Step 1: Simplify the fractions inside each root. For the first part: (16x^3y^9)/(2x^3) = (16 ÷ 2) · (x^3 ÷ x^3) · y^9 = 8 · 1 · y^9 = 8y^9 For the second part: (32y^8)/(9y^2) = (32)/(9) · (y^8 ÷ y^2) = (32y^6)/(9) For the third part: (98y^6)/(2) = (98 ÷ 2) · y^6 = 49y^6 Now the expression is: [3]8y^9 - sqrt((32y^6)/(9)) + sqrt(49y^6) Step 2: Take the cube root and square roots. For the first term, [3]8y^9: [3]8 · [3]y^9 = 2 · y^(9 ÷ 3) = 2y^3 For the second term, sqrt((32y^6)/(9)): sqrt(32y^6)sqrt(9) = sqrt(16 · 2 · y^6)3 = sqrt(16) · sqrt(2) · sqrt(y^6)3 = 4 · sqrt(2) · y^(6 ÷ 2)3 = 4y^3sqrt(2)3 For the third term, sqrt(49y^6): sqrt(49) · sqrt(y^6) = 7 · y^(6 ÷ 2) = 7y^3 Step 3: Combine the simplified terms. 2y^3 - 4y^3sqrt(2)3 + 7y^3 Combine the terms that have y^3: (2y^3 + 7y^3) - 4y^3sqrt(2)3 = 9y^3 - 4y^3sqrt(2)3 To combine these, write 9y^3 with a denominator of 3: (9 · 3)/(3)y^3 - 4sqrt(2)3y^3 = (27y^3)/(3) - 4sqrt(2)y^33 = 27y^3 - 4sqrt(2)y^33 = y^3(27 - 4sqrt(2))3 The final answer is y^3(27 - 4sqrt(2))3. Last free one today — make it count tomorrow, or type /upgrade for unlimited.