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
Huu hapa ni ufumbuzi wa swali lako la 5: Swali la 5: Bila kutumia jedwali za hisabati au kikokotoo, tathmini: ((81)/(16))^3/4 × ((27)/(64))^-2/3 Step 1: Rahisisha sehemu ya kwanza ya usemi. Tunajua kuwa 81 = 3^4 na 16 = 2^4. ((81)/(16))^3/4 = ((3^4)/(2^4))^3/4 = (((3)/(2))^4)^3/4 Tumia sheria ya vipeo (a^m)^n = a^mn: ((3)/(2))^4 × (3)/(4) = ((3)/(2))^3 = (3^3)/(2^3) = (27)/(8) Step 2: Rahisisha sehemu ya pili ya usemi. Tunajua kuwa 27 = 3^3 na 64 = 4^3. ((27)/(64))^-2/3 = ((3^3)/(4^3))^-2/3 = (((3)/(4))^3)^-2/3 Tumia sheria ya vipeo (a^m)^n = a^mn: ((3)/(4))^3 × (-(2)/(3)) = ((3)/(4))^-2 Tumia sheria ya vipeo hasi a^-n = (1)/(a^n) = ((1)/(a))^n: ((4)/(3))^2 = (4^2)/(3^2) = (16)/(9) Step 3: Zidisha matokeo ya sehemu zote mbili. (27)/(8) × (16)/(9) Rahisisha kwa kufuta namba zinazofanana: (27)/(9) × (16)/(8) = 3 × 2 = 6 Jibu la mwisho ni 6. That's 2 down. 3 left today — send the next one.