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
You're on a roll — Step 1: Simplify the expression (30x^4)/(3x^-2). We can separate the coefficients and the variables. (30x^4)/(3x^-2) = ((30)/(3)) × ((x^4)/(x^-2)) First, simplify the coefficients: (30)/(3) = 10 Next, simplify the terms with x using the rule (a^m)/(a^n) = a^m-n: (x^4)/(x^-2) = x^4 - (-2) = x^4+2 = x^6 Combine the simplified parts: 10 × x^6 = 10x^6 10x^6 Step 2: Simplify ((x^5)/(2t^3))^-4. Use the rule ((a)/(b))^-n = ((b)/(a))^n: ((x^5)/(2t^3))^-4 = ((2t^3)/(x^5))^4 Now, apply the power of 4 to each term in the numerator and the denominator using the rule (ab)^n = a^n b^n and (a^m)^n = a^mn: ((2t^3)/(x^5))^4 = ((2)^4 (t^3)^4)/((x^5)^4) Calculate the powers: (2)^4 = 2 × 2 × 2 × 2 = 16 (t^3)^4 = t^3 × 4 = t^12 (x^5)^4 = x^5 × 4 = x^20 Substitute these back into the expression: 16t^12x^20 16t^12x^20 Step 3: Simplify the powers: x^5 y^4 z^-4x^-2 y^2 z^-1. Apply the rule (a^m)/(a^n) = a^m-n to each variable separately: For x: (x^5)/(x^-2) = x^5 - (-2) = x^5+2 = x^7 For y: (y^4)/(y^2) = y^4-2 = y^2 For z: z^-4z^-1 = z^-4 - (-1) = z^-4+1 = z^-3 Combine the simplified terms. Use the rule a^-n = (1)/(a^n) for z^-3: x^7 y^2 z^-3 = (x^7 y^2)/(z^3) (x^7 y^2)/(z^3) Send me the next one 📸