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)
$$ \begin{aligned} & \frac{m^8 n^6}{m^4 n} \\ & =\left(m^8 \div m^4\right) \times\left(n^6 \div n\right) \\ & =m^{8-4} \times n^{6-1} \\ & =m^4 n^5 \end{aligned} $$
(d)
$$ \begin{aligned} & \frac{27 x^4 y^5}{9 x^3 y^2} \\ & =\frac{27}{9}\left(x^4 \div x^3\right)\left(y^5 \div y^2\right) \\ & =3\left(x^{4-3} \times y^{5-2}\right) \\ & =3 x y^3 \end{aligned} $$
(e)
$$ \begin{aligned} & m^7 \div m^2 \div m^4 \\ & =\left(m^{7-2}\right) \div m^4 \\ & =m^5 \div m^4 \\ & =m^{5-4} \\ & =m^1 \\ & =m \end{aligned} $$
(f)
$$ \begin{aligned} & -25 h^4 \div 5 h^2 \div h \\ & =(-25 \div 5)\left(h^4 \div h^2 \div h\right) \\ & =-5\left(h^{4-2}\right) \div h \\ & =-5 h^2 \div h \\ & =-5\left(h^{2-1}\right) \\ & =-5 h^1 \\ & =-5 h \end{aligned} $$
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)
$$ \begin{aligned} & \frac{m^8 n^6}{m^4 n} \\ & =\left(m^8 \div m^4\right) \times\left(n^6 \div n\right) \\ & =m^{8-4} \times n^{6-1} \\ & =m^4 n^5 \end{aligned} $$
(d)
$$ \begin{aligned} & \frac{27 x^4 y^5}{9 x^3 y^2} \\ & =\frac{27}{9}\left(x^4 \div x^3\right)\left(y^5 \div y^2\right) \\ & =3\left(x^{4-3} \times y^{5-2}\right) \\ & =3 x y^3 \end{aligned} $$
(e)
$$ \begin{aligned} & m^7 \div m^2 \div m^4 \\ & =\left(m^{7-2}\right) \div m^4 \\ & =m^5 \div m^4 \\ & =m^{5-4} \\ & =m^1 \\ & =m \end{aligned} $$
(f)
$$ \begin{aligned} & -25 h^4 \div 5 h^2 \div h \\ & =(-25 \div 5)\left(h^4 \div h^2 \div h\right) \\ & =-5\left(h^{4-2}\right) \div h \\ & =-5 h^2 \div h \\ & =-5\left(h^{2-1}\right) \\ & =-5 h^1 \\ & =-5 h \end{aligned} $$
Soalan 2:
Salin dan lengkapkan setiap persamaan di bawah.
Penyelesaian:
(a)
(b)
(c)
(d)
Salin dan lengkapkan setiap persamaan di bawah.
Penyelesaian:
(a)
(b)
(c)
(d)
Soalan 3:
$$ \text { Jika } \frac{2^x \times 3^y}{2^4 \times 3^2}=6 \text {, tentukan nilai } x+y \text {. } $$
Penyelesaian:
$$ \begin{aligned} \frac{2^x \times 3^y}{2^4 \times 3^2} & =6 \\ \left(2^x \div 2^4\right) \times\left(3^y \div 3^2\right) & =2 \times 3 \\ 2^{x-4} \times 3^{y-2} & =2^1 \times 3^1 \end{aligned} $$
$$ \begin{aligned} &\text { Bandingkan indeks bagi asas yang sama di kedua-dua belah }\\ &\begin{aligned} x-4 & =1 \\ x & =1+4 \\ x & =5 \end{aligned}\\ &\begin{aligned} y-2 & =1 \\ y & =1+2 \\ & =3 \end{aligned}\\ &\begin{aligned} x+y & =5+3 \\ & =8 \end{aligned} \end{aligned} $$
$$ \text { Jika } \frac{2^x \times 3^y}{2^4 \times 3^2}=6 \text {, tentukan nilai } x+y \text {. } $$
Penyelesaian:
$$ \begin{aligned} \frac{2^x \times 3^y}{2^4 \times 3^2} & =6 \\ \left(2^x \div 2^4\right) \times\left(3^y \div 3^2\right) & =2 \times 3 \\ 2^{x-4} \times 3^{y-2} & =2^1 \times 3^1 \end{aligned} $$
$$ \begin{aligned} &\text { Bandingkan indeks bagi asas yang sama di kedua-dua belah }\\ &\begin{aligned} x-4 & =1 \\ x & =1+4 \\ x & =5 \end{aligned}\\ &\begin{aligned} y-2 & =1 \\ y & =1+2 \\ & =3 \end{aligned}\\ &\begin{aligned} x+y & =5+3 \\ & =8 \end{aligned} \end{aligned} $$