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
Welcome back hanzalamillimo — missed you this week. To simplify the expression, we will first convert the division into multiplication by taking the reciprocal of the second fraction. Step 1: Rewrite the division as multiplication. (12dn^3)/(15cd^3) ÷ (9c^3n)/(10c^2d^2) = (12dn^3)/(15cd^3) × (10c^2d^2)/(9c^3n) Step 2: Multiply the numerators and the denominators. (12dn^3 × 10c^2d^2)/(15cd^3 × 9c^3n) Step 3: Group the numerical coefficients and the variables. ((12 × 10) × (d · d^2) × (n^3) × (c^2))/((15 × 9) × (c · c^3) × (d^3) × (n)) 120 d^1+2 n^3 c^2135 c^1+3 d^3 n (120 d^3 n^3 c^2)/(135 c^4 d^3 n) Step 4: Simplify the numerical coefficients by dividing by their greatest common divisor, which is 15. (120 ÷ 15)/(135 ÷ 15) = (8)/(9) Step 5: Simplify the variables using the exponent rule (x^a)/(x^b) = x^a-b. For d: (d^3)/(d^3) = d^3-3 = d^0 = 1 For n: (n^3)/(n) = n^3-1 = n^2 For c: (c^2)/(c^4) = c^2-4 = c^-2 = (1)/(c^2) Step 6: Combine the simplified numerical and variable parts. (8)/(9) × 1 × n^2 × (1)/(c^2) = (8n^2)/(9c^2) The simplified expression is: (8n^2)/(9c^2) Send me the next one 📸