Jawab: (i.) = -54 (ii) Nilai 2t = 24 ³√2 (iii) 7a³ × b⁴ × 3a² × b = 21a⁵b⁵
Penjelasan: (i.) Bila c = -2, d = 3, e = 4. [tex]\displaystyle\frac{c^{-5}d^3}{e^{-3}}=\frac{(-2)^{-5}\cdot3^3}{4^{-3}}\\\\\because n^{a}=\frac{1}{n^{-a}},\:\:\:n^{-a}=\frac{1}{n^a}\therefore\\\\\frac{(-2)^{-5}\cdot3^3}{4^{-3}}=\frac{4^3\cdot3^3}{(-2)^5}=-\frac{(2^2)^3\cdot3^3}{2^5}\\=-\frac{2^6\cdot3^3}{2^5}\:\:\:\because\frac{n^a}{n^b}=n^{a-b}\therefore\\\\-\frac{2^6\cdot3^3}{2^5}=-2^{6-5}\cdot3^3=2^{1}\cdot3^3\\-2\cdot27=-54[/tex]
(ii.) Bila [tex]\displaystyle t=81^{\frac{1}{4}}\times8^{\frac{1}{3}}\times4^{\frac{2}{3}}\\t=(3^4)^{\frac{1}{4}}\times(2^3)^{\frac{1}{3}}\times(2^2)^{\frac{2}{3}}\\t=3\times2\times2^{\frac{4}{3}}\\t=3\times2^{1+\frac{4}{3}}\\\because n^a\times n^b = n^{a+b}\therefore\\t=3\times2^{\frac{3}{3}+\frac{4}{3}}\\t=3\times2^{\frac{7}{3}}\\t=3\times2^{\frac{6}{3}+\frac{1}{3}}\\t=3\times2^{\frac{6}{3}}\times2^{\frac{1}{3}}\\t=3\times2^{2}\times\sqrt[3]{2}\\t=3\times4\times\sqrt[3]{2}\\t=12\times\sqrt[3]{2}[/tex] maka 2t = ..... [tex]2t=2(12\times\sqrt[3]{2})\\2t =24\:\sqrt[3]{2}[/tex]
Verified answer
Jawab:
(i.) = -54
(ii) Nilai 2t = 24 ³√2
(iii) 7a³ × b⁴ × 3a² × b = 21a⁵b⁵
Penjelasan:
(i.) Bila c = -2, d = 3, e = 4.
[tex]\displaystyle\frac{c^{-5}d^3}{e^{-3}}=\frac{(-2)^{-5}\cdot3^3}{4^{-3}}\\\\\because n^{a}=\frac{1}{n^{-a}},\:\:\:n^{-a}=\frac{1}{n^a}\therefore\\\\\frac{(-2)^{-5}\cdot3^3}{4^{-3}}=\frac{4^3\cdot3^3}{(-2)^5}=-\frac{(2^2)^3\cdot3^3}{2^5}\\=-\frac{2^6\cdot3^3}{2^5}\:\:\:\because\frac{n^a}{n^b}=n^{a-b}\therefore\\\\-\frac{2^6\cdot3^3}{2^5}=-2^{6-5}\cdot3^3=2^{1}\cdot3^3\\-2\cdot27=-54[/tex]
(ii.) Bila
[tex]\displaystyle t=81^{\frac{1}{4}}\times8^{\frac{1}{3}}\times4^{\frac{2}{3}}\\t=(3^4)^{\frac{1}{4}}\times(2^3)^{\frac{1}{3}}\times(2^2)^{\frac{2}{3}}\\t=3\times2\times2^{\frac{4}{3}}\\t=3\times2^{1+\frac{4}{3}}\\\because n^a\times n^b = n^{a+b}\therefore\\t=3\times2^{\frac{3}{3}+\frac{4}{3}}\\t=3\times2^{\frac{7}{3}}\\t=3\times2^{\frac{6}{3}+\frac{1}{3}}\\t=3\times2^{\frac{6}{3}}\times2^{\frac{1}{3}}\\t=3\times2^{2}\times\sqrt[3]{2}\\t=3\times4\times\sqrt[3]{2}\\t=12\times\sqrt[3]{2}[/tex]
maka 2t = .....
[tex]2t=2(12\times\sqrt[3]{2})\\2t =24\:\sqrt[3]{2}[/tex]
(iii) 7a³ × b⁴ × 3a² × b
= (7×3) × a³×a² × b⁴×b
∵ nᵃ × nᵇ = nᵃ⁺ᵇ
= 21 × a³⁺² × b⁴⁺¹
= 21 × a⁵ × b⁵
= 21a⁵b⁵
(xcvi)