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 — missed you this week. Here are the solutions for simplifying the algebraic expressions: 1) Simplify (6a^2 b^2)/(3a^5 b^3) Step 1: Simplify the coefficients and apply the exponent rule (x^m)/(x^n) = x^m-n to the variables. (6a^2 b^2)/(3a^5 b^3) = (6)/(3) · a^2-5 · b^2-3 Step 2: Perform the subtractions in the exponents and simplify the fraction. 2 · a^-3 · b^-1 Step 3: Rewrite terms with negative exponents using x^-n = (1)/(x^n). (2)/(a^3 b^1) (2)/(a^3 b) 2) Simplify (45x^3 b^7)/(3x^4 b^2) Step 1: Simplify the coefficients and apply the exponent rule (x^m)/(x^n) = x^m-n to the variables. (45x^3 b^7)/(3x^4 b^2) = (45)/(3) · x^3-4 · b^7-2 Step 2: Perform the subtractions in the exponents and simplify the fraction. 15 · x^-1 · b^5 Step 3: Rewrite terms with negative exponents using x^-n = (1)/(x^n). (15b^5)/(x^1) (15b^5)/(x) 3) Simplify (21t^3 y + 7t^2 y^2 + 28ty^7)/(14t^5 y^3) Step 1: Divide each term in the numerator by the denominator. (21t^3 y)/(14t^5 y^3) + (7t^2 y^2)/(14t^5 y^3) + (28ty^7)/(14t^5 y^3) Step 2: Simplify each fraction by dividing coefficients and applying the exponent rule (x^m)/(x^n) = x^m-n. (3)/(2) t^3-5 y^1-3 + (1)/(2) t^2-5 y^2-3 + (2)/(1) t^1-5 y^7-3 (3)/(2) t^-2 y^-2 + (1)/(2) t^-3 y^-1 + 2 t^-4 y^4 Step 3: Rewrite terms with negative exponents using x^-n = (1)/(x^n). (3)/(2t^2 y^2) + (1)/(2t^3 y) + (2y^4)/(t^4) (3)/(2t^2 y^2) + (1)/(2t^3 y) + (2y^4)/(t^4) 4) Simplify (33p^0 z^3 - 11p^2 z^3)/(22p^5 z^2) Step 1: Simplify p^0 = 1. (33(1)z^3 - 11p^2 z^3)/(22p^5 z^2) = (33z^3 - 11p^2 z^3)/(22p^5 z^2) Step 2: Divide each term in the numerator by the denominator. (33z^3)/(22p^5 z^2) - (11p^2 z^3)/(22p^5 z^2) Step 3: Simplify each fraction by dividing coefficients and applying the exponent rule (x^m)/(x^n) = x^m-n. (3)/(2) p^0-5 z^3-2 - (1)/(2) p^2-5 z^3-2 (3)/(2) p^-5 z^1 - (1)/(2) p^-3 z^1 Step 4: Rewrite terms with negative exponents using x^-n = (1)/(x^n). (3z)/(2p^5) - (z)/(2p^3) (3z)/(2p^5) - (z)/(2p^3) Drop the next question!