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)
$$ \begin{aligned} & \frac{\sqrt[3]{c^2 d^3 e} \times c^{\frac{1}{3}} d^2 e^{\frac{2}{3}}}{\left(c^{-3} d^2 \mathrm{e}\right)^2} \\ & =\frac{\left(c^2 d^3 e\right)^{\frac{1}{3}} \times c^{\frac{1}{3}} d^2 e^{\frac{2}{3}}}{c^{-3 \times 2} d^{2 \times 2} e^{1 \times 2}} \\ & =\frac{c^{2 \times \frac{1}{3}} d^{3 \times \frac{1}{3}} e^{1 \times \frac{1}{3}} \times c^{\frac{1}{3}} d^2 e^{\frac{2}{3}}}{c^{-6} d^4 e^2} \end{aligned} $$
$$ \begin{aligned} & =\frac{c^{\frac{2}{3}} d^{\frac{3}{3}} e^{\frac{1}{3}} \times c^{\frac{1}{3}} d^2 e^{\frac{2}{3}}}{c^{-6} d^4 e^2} \\ & =c^{\frac{2}{3}+\frac{1}{3}-(-6)} \times d^{1+2-4} \times e^{\frac{1}{3}+\frac{2}{3}-2} \\ & =c^7 \times d^{-1} \times e^{-1} \\ & =\frac{c^7}{d e} \end{aligned} $$
(b)
$$ \begin{aligned} & \frac{\left(m n^2\right)^3 \times(\sqrt{m n})^4}{\left(m^6 n^3\right)^{\frac{2}{3}}} \\ & =\frac{m^{1 \times 3} n^{2 \times 3} \times\left((m n)^{\frac{1}{2}}\right)^4}{m^{6 \times \frac{2}{3}} n^{3 \times \frac{2}{3}}} \\ & =\frac{m^3 n^6 \times\left(m^{\frac{1}{2}} n^{\frac{1}{2}}\right)^4}{m^4 n^2} \end{aligned} $$
$$ \begin{aligned} & =\frac{m^3 n^6 \times m^{\frac{1}{2} \times 4} n^{\frac{1}{2} \times 4}}{m^4 n^2} \\ & =\frac{m^3 n^6 \times m^2 n^2}{m^4 n^2} \\ & =m^{3+2-4} \times n^{6+2-2} \\ & =m n^6 \end{aligned} $$
(c)
$$ \begin{aligned} & \frac{\sqrt{25 x^3 y z^2} \times 4 x^2 z}{\sqrt{36 x^5 y z^8}} \\ & =\frac{\left(25 x^3 y z^2\right)^{\frac{1}{2}} \times 4 x^2 z}{\left(36 x^5 y z^8\right)^{\frac{1}{2}}} \\ & =\frac{25^{\frac{1}{2}} x^{\frac{3}{2}} y^{\frac{1}{2}} z^{\frac{2}{2}} \times 4 x^2 z}{36^{\frac{1}{2}} x^{\frac{5}{2}} y^{\frac{1}{2}} z^{\frac{8}{2}}} \end{aligned} $$
$$ \begin{aligned} & =\frac{5 x^{\frac{3}{2}} y^{\frac{1}{2}} z \times 4 x^2 z}{6 x^{\frac{5}{2}} y^{\frac{1}{2}} z^4} \\ & =\frac{5 \times 4}{6} \times x^{\frac{3}{2}+2-\frac{5}{2}} \times y^{\frac{1}{2}-\frac{1}{2}} \times z^{1+1-4} \\ & =\frac{10}{3} x y^0 z^{-2} \\ & =\frac{10 x}{3 z^2} \end{aligned} $$
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)
$$ \begin{aligned} & \frac{\sqrt[3]{c^2 d^3 e} \times c^{\frac{1}{3}} d^2 e^{\frac{2}{3}}}{\left(c^{-3} d^2 \mathrm{e}\right)^2} \\ & =\frac{\left(c^2 d^3 e\right)^{\frac{1}{3}} \times c^{\frac{1}{3}} d^2 e^{\frac{2}{3}}}{c^{-3 \times 2} d^{2 \times 2} e^{1 \times 2}} \\ & =\frac{c^{2 \times \frac{1}{3}} d^{3 \times \frac{1}{3}} e^{1 \times \frac{1}{3}} \times c^{\frac{1}{3}} d^2 e^{\frac{2}{3}}}{c^{-6} d^4 e^2} \end{aligned} $$
$$ \begin{aligned} & =\frac{c^{\frac{2}{3}} d^{\frac{3}{3}} e^{\frac{1}{3}} \times c^{\frac{1}{3}} d^2 e^{\frac{2}{3}}}{c^{-6} d^4 e^2} \\ & =c^{\frac{2}{3}+\frac{1}{3}-(-6)} \times d^{1+2-4} \times e^{\frac{1}{3}+\frac{2}{3}-2} \\ & =c^7 \times d^{-1} \times e^{-1} \\ & =\frac{c^7}{d e} \end{aligned} $$
(b)
$$ \begin{aligned} & \frac{\left(m n^2\right)^3 \times(\sqrt{m n})^4}{\left(m^6 n^3\right)^{\frac{2}{3}}} \\ & =\frac{m^{1 \times 3} n^{2 \times 3} \times\left((m n)^{\frac{1}{2}}\right)^4}{m^{6 \times \frac{2}{3}} n^{3 \times \frac{2}{3}}} \\ & =\frac{m^3 n^6 \times\left(m^{\frac{1}{2}} n^{\frac{1}{2}}\right)^4}{m^4 n^2} \end{aligned} $$
$$ \begin{aligned} & =\frac{m^3 n^6 \times m^{\frac{1}{2} \times 4} n^{\frac{1}{2} \times 4}}{m^4 n^2} \\ & =\frac{m^3 n^6 \times m^2 n^2}{m^4 n^2} \\ & =m^{3+2-4} \times n^{6+2-2} \\ & =m n^6 \end{aligned} $$
(c)
$$ \begin{aligned} & \frac{\sqrt{25 x^3 y z^2} \times 4 x^2 z}{\sqrt{36 x^5 y z^8}} \\ & =\frac{\left(25 x^3 y z^2\right)^{\frac{1}{2}} \times 4 x^2 z}{\left(36 x^5 y z^8\right)^{\frac{1}{2}}} \\ & =\frac{25^{\frac{1}{2}} x^{\frac{3}{2}} y^{\frac{1}{2}} z^{\frac{2}{2}} \times 4 x^2 z}{36^{\frac{1}{2}} x^{\frac{5}{2}} y^{\frac{1}{2}} z^{\frac{8}{2}}} \end{aligned} $$
$$ \begin{aligned} & =\frac{5 x^{\frac{3}{2}} y^{\frac{1}{2}} z \times 4 x^2 z}{6 x^{\frac{5}{2}} y^{\frac{1}{2}} z^4} \\ & =\frac{5 \times 4}{6} \times x^{\frac{3}{2}+2-\frac{5}{2}} \times y^{\frac{1}{2}-\frac{1}{2}} \times z^{1+1-4} \\ & =\frac{10}{3} x y^0 z^{-2} \\ & =\frac{10 x}{3 z^2} \end{aligned} $$