Indeks

Soalan 1:Hitung nilai setiap yang berikut.Penyelesaian:(a)$$ 27^{\frac{2}{3}}=(\sqrt[3]{27})^2=(3)^2=9 $$(b)$$ 32^{\frac{2}{5}}=(\sqrt[5]{32})^2=(2)^2=4 $$(c)(d)(e)$$ 64^{\frac{4}{3}}=\left(4^3\right)^{\frac{4}{3}}=(4)^4=256 $$(f)$$ 1024^{\frac{2}{5}}=\left(4^5\right)^{\frac{2}{8}}=(4)^2=16 $$(g)$$ 1296^{\frac{3}{4}}=\left(6^4\right)^{\frac{3}{4}}=(6)^3=216 $$(h)$$ 49^{\frac{3}{2}}=\left(7^2\right)^{\frac{3}{2}}=(7)^3=343 $$(i)$$ 2401^{\frac{1}{4}}=\left(7^4\right)^{\frac{1}{\frac{4}{4}}}=(7)^1=7 $$(j)$$ 121^{\frac{3}{2}}=\left(11^2\right)^{\frac{3}{2}}=(11)^3=1331 $$(k)$$ 2197^{\frac{2}{3}}=\left(13^3\right)^{\frac{2}{3}}=(13)^2=169 $$(l)$$ 10000^{\frac{3}{4}}=\left(10^4\right)^{\frac{3}{4}}=(10)^3=1000 $$

Soalan 1:Lengkapkan jadual di bawah.Penyelesaian:

Soalan 1:Penyelesaian:$$ \begin{aligned} &\begin{aligned} & \sqrt[2]{x}=x^{\frac{1}{2}} \\ & \sqrt[3]{x}=x^{\frac{1}{3}} \end{aligned}\\ &\text { Secara generalisasi, }\\ &\sqrt[n]{a}=a^{\frac{1}{n}} ; a \neq 0 \end{aligned} $$(a)$$ \sqrt[3]{125}=125^{\frac{1}{3}} $$ (b)$$ \sqrt[7]{2187}=2187^{\frac{1}{7}} $$(c)$$ \sqrt[5]{-1024}=(-1024)^{\frac{1}{5}} $$(d)$$ \sqrt[10]{n}=n^{\frac{1}{10}} $$ Soalan 2: Penyelesaian:(a)$$ 4^{\frac{1}{2}}=\sqrt{4} $$(b)$$ 32^{\frac{1}{5}}=\sqrt[5]{32} $$(c)$$ (-729)^{\frac{1}{3}}=\sqrt[3]{-729} $$(d)$$ n^{\frac{1}{15}}=\sqrt[15]{n} $$ Soalan 3: Penyelesaian:(a)$$ \begin{aligned} \sqrt[3]{343} & =343^{\frac{1}{3}} \\ & =\left(7^3\right)^{\frac{1}{3}} \\ & =7^{\frac{3}{3}} … Read more

Soalan 1:Nyatakan setiap sebutan berikut dalam bentuk indeks positif. Penyelesaian:(a)$$ 5^{-3}=\frac{1}{5^3} $$(b)$$ 8^{-4}=\frac{1}{8^4} $$(c)$$ x^{-8}=\frac{1}{x^8} $$(d)$$ y^{-16}=\frac{1}{y^{16}} $$(e) $$ \frac{1}{a^{-4}}=a^4 $$(f)$$ \frac{1}{20^{-2}}=20^2 $$ (g)$$ 3 n^{-4}=3\left(\frac{1}{n^4}\right)=\frac{3}{n^4} $$(h)$$ -5 n^{-6}=-5\left(\frac{1}{n^6}\right)=-\frac{5}{n^6} $$(i)$$ \frac{2}{7} m^{-5}=\frac{2}{7}\left(\frac{1}{m^5}\right)=\frac{2}{7 m^5} $$ (j) $$ \left(-\frac{3}{8}\right) m^{-4}=\left(-\frac{3}{8}\right)\left(\frac{1}{m^4}\right)=-\frac{3}{8 m^4} $$(k)$$ \left(\frac{2}{5}\right)^{-12}=\left(\frac{5}{2}\right)^{12} $$(l)$$ \left(-\frac{3}{7}\right)^{-14}=\left(-\frac{7}{3}\right)^{14} $$ (m)$$ \left(\frac{x}{y}\right)^{-10}=\left(\frac{y}{x}\right)^{10} $$(n)$$ \left(\frac{2 x}{3 y}\right)^{-4}=\left(\frac{3 y}{2 x}\right)^4 $$(o)$$ \left(\frac{1}{2 x}\right)^{-5}=(2 … Read more

Soalan 1:Ringkaskan setiap yang berikut. Penyelesaian:(a)$$ \begin{aligned} & \left(2 \times 3^4\right)^2 \\ & =2^{1(2)} \times 3^{4(2)} \\ & =2^2 \times 3^8 \end{aligned} $$(b)$$ \begin{aligned} & \left(11^3 \times 9^5\right)^3 \\ & =11^{3(3)} \times 9^{5(3)} \\ & =11^9 \times 9^{15} \end{aligned} $$ (c)$$ \begin{aligned} & \left(13^3 \div 7^6\right)^2 \\ & =13^{3(2)} \div 7^{6(2)} \\ & =13^6 \div … Read more

Soalan 1:Gunakan hukum indeks untuk meringkaskan setiap pernyataan berikut.(a) (125)2 (b) (310)2 (c) (72)3(d) ((– 4)3)7(e) (k8)3(f) (g2)13(g) ((–m)4)3(h) ((–c)7)3 Penyelesaian:(a)$$ \begin{aligned} & \left(12^5\right)^2 \\ & =12^{5(2)} \\ & =12^{10} \end{aligned} $$ (b) $$ \begin{aligned} & \left(3^{10}\right)^2 \\ & =3^{10(2)} \\ & =3^{20} \end{aligned} $$ (c) $$ \begin{aligned} & \left(7^2\right)^3 \\ & =7^{2(3)} \\ & … Read more

Soalan 1:Permudahkan setiap yang berikut. Penyelesaian:(a)$$ \begin{aligned} & 4^5 \div 4^4 \\ & =4^{5-4} \\ & =4^1 \\ & =4 \end{aligned} $$(b)$$ \begin{aligned} & 7^{10} \div 7^6 \div 7^2 \\ & =7^{10-6} \div 7^2 \\ & =7^{4-2} \\ & =7^2 \end{aligned} $$ (c)$$ \begin{aligned} & \frac{m^8 n^6}{m^4 n} \\ & =\left(m^8 \div m^4\right) \times\left(n^6 \div … Read more

Soalan 1:Nyatakan dalam bentuk indeks paling ringkas.$$ \text { (a) } 5^4 \times 9^3 \times 5 \times 9^2 $$$$ \text { (b) }(0.4)^2 \times(1.2)^3 \times(0.4) \times(1.2)^5 \times(1.2) $$$$ \text { (c) } 12 x^5 \times y^3 \times \frac{1}{2} x \times \frac{2}{3} y^4 $$$$ \text { (d) }-2 k^5 \times p^6 \times \frac{1}{4} p^5 \times 3 … Read more

Soalan 1:Permudahkan setiap yang berikut. $$ \text { (a) } 3^2 \times 3 \times 3^4 $$ $$ \text { (b) }(-0.4)^4 \times(-0.4)^3 \times(-0.4) $$$$ \text { (c) }\left(\frac{4}{7}\right) \times\left(\frac{4}{7}\right)^3 \times\left(\frac{4}{7}\right)^5 $$$$ \text { (d) }\left(-1 \frac{2}{5}\right)^2 \times\left(-1 \frac{2}{5}\right)^3 \times\left(-1 \frac{2}{5}\right)^5 $$$$ \text { (e) } 4 m^2 \times \frac{1}{2} m^3 \times(-3) m^4 $$$$ \text { … Read more

Soalan 14: Diberi  k 3 = 9 − 3 2 × 64 1 2 , cari nilai bagi k. Penyelesaian: k 3 = 9 − 3 2 × 64 1 2    = ( 3 2 ) − 3 2 × ( 2 6 ) 1 2    = 3 −3 × 2 3    = ( 2 3 ) 3 k= … Read more