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
O dara, jẹ ki a rọrun awọn ikosile wọnyi ni lilo awọn ofin exponents. 1. Rọrun (6^3)/(6^4) Step 1: Lo ofin ipin fun exponents, eyiti o sọ pe (a^m)/(a^n) = a^m-n. (6^3)/(6^4) = 6^3-4 Step 2: Ṣe iṣiro exponent naa. 6^3-4 = 6^-1 Step 3: Ranti pe a^-n = (1)/(a^n). 6^-1 = (1)/(6) 2. Rọrun (28m^4n^6)/(7m^3n^2) Step 1: Pin awọn nọmba (coefficients) ati lo ofin ipin fun awọn oniyipada kọọkan. (28m^4n^6)/(7m^3n^2) = ((28)/(7)) × ((m^4)/(m^3)) × ((n^6)/(n^2)) Step 2: Ṣe iṣiro ipin kọọkan. 4 × m^4-3 × n^6-2 Step 3: Ṣe iṣiro awọn exponents. 4 × m^1 × n^4 = 4mn^4 3. Rọrun (4x^5)^3 Step 1: Lo ofin agbara ọja, eyiti o sọ pe (ab)^m = a^m b^m. (4x^5)^3 = 4^3 × (x^5)^3 Step 2: Lo ofin agbara agbara, eyiti o sọ pe (a^m)^n = a^m × n. 4^3 × x^5 × 3 Step 3: Ṣe iṣiro awọn agbara. 64 × x^15 = 64x^15 4. Rọrun 4^3 × 4^2 Step 1: Lo ofin isodipupo fun exponents, eyiti o sọ pe a^m × a^n = a^m+n. 4^3 × 4^2 = 4^3+2 Step 2: Ṣe iṣiro exponent naa. 4^3+2 = 4^5 Step 3: Ṣe iṣiro agbara naa. 4^5 = 4 × 4 × 4 × 4 × 4 = 1024 1024 5. Rọrun (5^-2)^3 Step 1: Lo ofin agbara agbara, eyiti o sọ pe (a^m)^n = a^m × n. (5^-2)^3 = 5^-2 × 3 Step 2: Ṣe iṣiro exponent naa. 5^-6 Step 3: Ranti pe a^-n = (1)/(a^n). 5^-6 = (1)/(5^6) That's 2 down. 3 left today — send the next one.