Soalan 1:Nyatakan sama ada operasi yang melibatkan hukum indeks berikut benar atau palsu. Jika palsu, nyatakan jawapan yang betul.Penyelesaian:(a)$$ \begin{aligned} &a^5=a \times a \times a \times a \times a\\ &\text { berulang lima kali } \end{aligned} $$$$ \begin{aligned} &a^5=a^5\\ &\text { Benar } \end{aligned} $$(b)$$ \begin{aligned} & 5^2=10 \\ & 5^2=5 \times 5 \\ &=25 … Read more

Soalan 3:$$ \text { Diberi bahawa } m=2 \text { dan } n=-3 \text {. Hitung nilai bagi } 64^{\frac{m}{3}} \times 512^{\left(-\frac{1}{n}\right)} \div 81^{\frac{n}{2 m}} \text {. } $$Penyelesaian:$$ \begin{aligned} &64^{\frac{m}{3}} \times 512^{\left(-\frac{1}{n}\right)} \div 81^{\frac{n}{2 m}}\\ &\text { Diberi } m=2 \text { dan } n=-3 \end{aligned} $$$$ \begin{aligned} 64^{\frac{2}{3}} \times 512\left(-\frac{1}{-3}\right) \div 81^{\frac{-3}{2(2)}} & … Read more

Soalan 2:Hitung nilai setiap yang berikut.$$ \text { (a) } \frac{\sqrt{7^{-4} \times 11^4}}{49 \times 121} $$$$ \text { (b) } \frac{\left(5^{-3} \times 3^6\right)^{\frac{1}{3}} \times \sqrt[4]{16}}{(125 \times 729 \times 64)^{-\frac{1}{3}}} $$$$ \text { (c) } \frac{\left(2^6 \times 3^4 \times 5^2\right)^{\frac{3}{2}}}{\sqrt[4]{256} \times \sqrt{729} \times \sqrt[3]{125}} $$$$ \text { (d) } \frac{9 \sqrt{512} \times \sqrt[3]{343} \times \sqrt{121}}{(64)^{\frac{1}{3}} \times(81)^{\frac{3}{4}} … Read more

Soalan 1:Permudahkan setiap yang berikut.$$ \text { (a) } \frac{\sqrt[3]{c^2 d^3 e} \times c^{\frac{1}{3}} d^2 e^{\frac{2}{3}}}{\left(c^{-3} d^2 e\right)^2} $$$$ \text { (b) } \frac{\left(m n^2\right)^3 \times(\sqrt{m n})^4}{\left(m^6 n^3\right)^{\frac{2}{3}}} $$$$ \text { (c) } \frac{\sqrt{25 x^3 y z^2} \times 4 x^2 z}{\sqrt{36 x^5 y z^8}} $$Penyelesaian:(a)$$ \begin{aligned} & \frac{\sqrt[3]{c^2 d^3 e} \times c^{\frac{1}{3}} d^2 e^{\frac{2}{3}}}{\left(c^{-3} d^2 … Read more

Soalan 2:Lengkapkan rajah berikut dengan nilai yang betul.Penyelesaian:(a)$$ \begin{aligned} \sqrt[y]{6561^x} & =81 \\ 6561^{\frac{x}{y}} & =3^4 \\ \left(3^8\right)^{\frac{x}{y}} & =3^4 \\ (3)^{\frac{8 x}{y}} & =3^4 \\ \frac{8 x}{y} & =4 \\ \frac{x}{y} & =\frac{4}{8} \\ \frac{x}{y} & =\frac{1}{2} \\ x & =1, y=2 \\ \therefore \sqrt[2]{6561^1} & =81 \end{aligned} $$$$ \begin{aligned} 3^x & =81 \\ … Read more

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