a) i) Evaluate 27^(2/3) ii) Simplify 6(x4)y5 / 12y4y5 iii) Solve p^-8 x p4 = 1/9 iv) Express 6004.83 in standard form.

Haya hapa masuluhisho ya maswali yako: a) i) Evaluate 27^(2)/(3) Step 1: Andika 27 kama kielelezo cha 3. 27 = 3^3 Step 2: Badilisha 27 na 3^3 katika usemi na tumia sheria ya vipeo (a^m)^n = a^mn. 27^(2)/(3) = (3^3)^(2)/(3) = 3^3 × (2)/(3) Step 3: Rahisisha kielelezo na hesabu. 3^3 × (2)/(3) = 3^2 = 9 Jibu ni 9. ii) Simplify (6(y^4)^5)/(12y^4y^5) Step 1: Rahisisha kielelezo cha juu kwa kutumia sheria (a^m)^n = a^mn. (6(y^4)^5)/(12y^4y^5) = 6y^4 × 512y^4y^5 = 6y^2012y^4y^5 Step 2: Rahisisha vipeo vya y kwenye denominator kwa kutumia sheria a^m × a^n = a^m+n. 6y^2012y^4y^5 = 6y^2012y^4+5 = 6y^2012y^9 Step 3: Rahisisha sehemu ya namba na vipeo vya y kwa kutumia sheria (a^m)/(a^n) = a^m-n. (6)/(12) × y^20y^9 = (1)/(2) × y^20-9 = (1)/(2)y^11 Jibu ni (1)/(2)y^11. iii) Solve p^-8 × p^(1)/(4) = (1)/(9) Step 1: Tumia sheria ya vipeo a^m × a^n = a^m+n upande wa kushoto. p^-8 × p^(1)/(4) = p^-8 + (1)/(4) Step 2: Rahisisha kielelezo. -8 + (1)/(4) = -(32)/(4) + (1)/(4) = -(31)/(4) Hivyo, mlinganyo unakuwa: p^-(31)/(4) = (1)/(9) Step 3: Andika (1)/(9) kama kielelezo cha 3. (1)/(9) = (1)/(3^2) = 3^-2 Hivyo, mlinganyo unakuwa: p^-(31)/(4) = 3^-2 Step 4: Ili kupata p, inua pande zote mbili kwa kielelezo cha kinyume cha -(31)/(4), ambacho ni -(4)/(31). (p^-(31)/(4))^-(4)/(31) = (3^-2)^-(4)/(31) p^ (-(31)/(4)) × (-(4)/(31)) = 3^ (-2) × (-(4)/(31)) p^1 = 3^(8)/(31) Jibu ni p = 3^(8)/(31). iv) Express 6004.83 in standard form. Step 1: Hamisha desimali ili namba iwe kati ya 1 na 10. Namba 6004.83 inakuwa 6.00483. Step 2: Hesabu idadi ya sehemu ambazo desimali imesogezwa. Desimali imesogezwa sehemu 3 kwenda kushoto. Hii inamaanisha tunazidisha na 10^3. Step 3: Andika namba katika mfumo wa kawaida a × 10^n. 6004.83 = 6.00483 × 10^3 Jibu ni 6.00483 × 10^3. Tuma swali linalofuata 📸