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 la 22. Swali la 22: A digital display records the number of operations carried out by a computer as 2^n × 2^1. a) Rahisisha usemi, ukiacha jibu lako katika fomu ya 'index'. Step 1: Tumia sheria ya 'indices' inayosema kwamba unapozidisha namba zenye 'base' sawa, unaongeza 'powers' zake: a^m × a^n = a^m+n. 2^n × 2^1 = 2^n+1 Jibu ni 2^n+1. b) Kwa hivyo, andika jibu kama nambari ya kawaida. Haiwezekani kuandika 2^n+1 kama nambari ya kawaida bila kujua thamani maalum ya 'n'. c) Rahisisha: (5^4 × 5^4)/(5^3) Step 1: Rahisisha nambari ya juu (numerator) kwa kutumia sheria ya 'indices' a^m × a^n = a^m+n. 5^4 × 5^4 = 5^4+4 = 5^8 Step 2: Rahisisha usemi mzima kwa kutumia sheria ya 'indices' inayosema kwamba unapotenganisha namba zenye 'base' sawa, unatoa 'powers' zake: (a^m)/(a^n) = a^m-n. (5^8)/(5^3) = 5^8-3 = 5^5 Jibu ni 5^5. 3 done, 2 left today. You're making progress.