Cabaran Dinamis 1 – Mahir Diri (Soalan 1 & 2) – Buku Teks Matematik Tingkatan 3 Bab 1 (Indeks)

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)
$$\begin{aligned} & \left(m n^4\right)^3 \div m^4 n^5 \\ & =\frac{\left(m n^4\right)^3}{m^4 n^5} \\ & =\frac{m^3 n^{12}}{m^4 n^5} \\ & =m^{3-4} n^{12-5} \\ & =m^{-1} n^7 \\ & =\frac{n^7}{m} \end{aligned}$$

(b)
$$\begin{aligned} & 3 x \times \frac{1}{6} y^4 \times(x y)^3 \\ & =(3)\left(\frac{1}{6}\right)(x)\left(y^4\right)\left(x^3\right)\left(y^3\right) \\ & =\frac{1}{2} x^{1+3} y^{4+3} \\ & =\frac{1}{2} x^4 y^7 \\ & =\frac{x^4 y^7}{2} \end{aligned}$$

(c)
$$\begin{aligned} & \sqrt{x y} \times \sqrt[3]{x y^2} \times \sqrt[6]{x y^5} \\ & =x^{\frac{1}{2}} y^{\frac{1}{2}} \times\left(x^{\frac{1}{3}}\right)\left(y^2\right)^{\frac{1}{3}} \times\left(x^{\frac{1}{6}}\right)\left(y^5\right)^{\frac{1}{6}} \\ & =x^{\frac{1}{2}} y^{\frac{1}{2}} \times x^{\frac{1}{3}} y^{\frac{2}{3}} \times x^{\frac{1}{6}} y^{\frac{5}{6}} \\ & =x^{\frac{1}{2}+\frac{1}{3}+\frac{1}{6}} y^{\frac{1}{2}+\frac{2}{3}+\frac{5}{6}} \\ & =x^{\frac{3}{6}+\frac{2}{6}+\frac{1}{6}} y^{\frac{3}{6}+\frac{4}{6}+\frac{5}{6}} \\ & =x^{\frac{6}{6}} y^{\frac{12}{6}} \\ & =x y^2 \end{aligned}$$

Soalan 2:
Hitung nilai setiap yang berikut.
$$\text { (a) } 64^{\frac{1}{3}} \times 5^{-3}$$
$$\text { (b) } 7^{-1} \times 125^{\frac{2}{3}}$$
$$\text { (c) }(256)^{\frac{3}{8}} \times 2^{-3}$$
$$\text { (d) } 2^4 \times 16^{-\frac{3}{4}}$$
$$\text { (e) } \sqrt{49} \times 3^{-2} \div(\sqrt{81})^{-1}$$
$$\text { (f) }(125)^{\frac{2}{3}} \times(25)^{-\frac{3}{2}} \div(625)^{-\frac{1}{4}}$$

Penyelesaian:
(a)
$$\begin{aligned} & 64^{\frac{1}{3}} \times 5^{-3} \\ & =\left(4^3\right)^{\frac{1}{3}} \times 5^{-3} \\ & =4^1 \times \frac{1}{5^3} \\ & =\frac{4}{5^3} \\ & =\frac{4}{125} \end{aligned}$$
(b)
$$\begin{aligned} & 7^{-1} \times 125^{\frac{2}{3}} \\ & =7^{-1} \times\left(5^3\right)^{\frac{2}{3}} \\ & =\frac{1}{7} \times 5^2 \\ & =\frac{25}{7} \end{aligned}$$

(c)
$$\begin{aligned} & (256)^{\frac{3}{8}} \times 2^{-3} \\ & =\left(2^8\right)^{\frac{3}{8}} \times 2^{-3} \\ & =2^3 \times 2^{-3} \\ & =2^{3+(-3)} \\ & =2^{3-3} \\ & =2^0 \\ & =1 \end{aligned}$$
(d)
$$\begin{aligned} & 2^4 \times 16^{-\frac{3}{4}} \\ = & 2^4 \times\left(2^4\right)^{-\frac{3}{4}} \\ = & 2^4 \times 2^{-3} \\ = & 2^{4-3} \\ = & 2 \end{aligned}$$

(e)
$$\begin{aligned} & \sqrt{49} \times 3^{-2} \div(\sqrt{81})^{-1} \\ & =7 \times \frac{1}{3^2} \div \frac{1}{\sqrt{81}} \\ & =7 \times \frac{1}{9} \times \sqrt{81} \\ & =\frac{7}{9} \times 9 \\ & =7 \end{aligned}$$
(f)
$$\begin{aligned} & (125)^{\frac{2}{3}} \times(25)^{-\frac{3}{2}} \div(625)^{-\frac{1}{4}} \\ & =\left(5^3\right)^{\frac{2}{3}} \times\left(5^2\right)^{-\frac{3}{2}} \div\left(5^4\right)^{-\frac{1}{4}} \\ & =5^2 \times 5^{-3} \div 5^{-1} \\ & =5^{2+(-3)-(-1)} \\ & =5^{2-3+1} \\ & =5^0 \\ & =1 \end{aligned}$$