Soalan 3:Hitung nilai-nilai x yang mungkin bagi setiap persamaan berikut.$$ \text { (a) } a^{x^2} \div a^{5 x}=\mathrm{a}^6 $$$$ \text { (b) } 2^{x^2} \times 2^{6 x}=2^7 $$$$ \text { (c) } 5^{x^2} \div 5^{3 x}=625 $$Penyelesaian:(a)$$ \begin{aligned} a^{x^2} \div a^{5 x} & =a^6 \\ a^{x^2-5 x} & =a^6 \\ x^2-5 x & =6 \\ … Read more

Soalan 1:Hitung nilai setiap yang berikut tanpa menggunakan kalkulator.$$ \text { (a) } 4^{\frac{1}{3}} \times 50^{\frac{2}{3}} \times 10^{\frac{5}{3}} $$$$ \text { (b) } 5^{\frac{5}{2}} \times 20^{\frac{3}{2}} \div 10^{-2} $$$$ \text { (c) } 60^{\frac{1}{2}} \times 125^{\frac{2}{3}} \div \sqrt{15} $$Penyelesaian:(a)$$ \begin{aligned} & 4^{\frac{1}{3}} \times 50^{\frac{2}{3}} \times 10^{\frac{5}{3}} \\ & =\left(2^2\right)^{\frac{1}{3}} \times\left(2^1 \times 5^2\right)^{\frac{2}{3}} \times\left(2^1 \times 5^1\right)^{\frac{5}{3}} … Read more

Soalan 3:Hitung nilai x bagi setiap persamaan berikut.$$ \text { (a) } 2^6 \div 2^x=8 $$$$ \text { (b) } 3^{-4} \times 81=3^x $$$$ \text { (c) } a^x a^8=1 $$$$ \text { (d) } 4 \times 8^{x+1}=2^{2 x} $$$$ \text { (e) }\left(a^x\right)^2 \times a^5=a^{3 x} $$$$ \text { (f) } 2^x=\frac{2^{10}}{16^x} $$$$ \text … Read more

Soalan 1:Ringkaskan setiap yang berikut.$$ \text { (a) }\left(m n^4\right)^3 \div m^4 n^5 $$$$ \text { (b) } 3 x \times \frac{1}{6} y^4 \times(x y)^3 $$$$ \text { (c) } \sqrt{x y} \times \sqrt[3]{x y^2} \times \sqrt[6]{x y^5} $$Penyelesaian:(a)$$ \begin{aligned} & \left(m n^4\right)^3 \div m^4 n^5 \\ & =\frac{\left(m n^4\right)^3}{m^4 n^5} \\ & =\frac{m^3 n^{12}}{m^4 … Read more

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)$$ 10000^{\frac{3}{4}}=\left(10^4\right)^{\frac{3}{4}}=(10)^3=1000 $$