Soalan 1:
Nyatakan dalam bentuk indeks paling ringkas.
$$ \text { (a) } 5^4 \times 9^3 \times 5 \times 9^2 $$
$$ \text { (b) }(0.4)^2 \times(1.2)^3 \times(0.4) \times(1.2)^5 \times(1.2) $$
$$ \text { (c) } 12 x^5 \times y^3 \times \frac{1}{2} x \times \frac{2}{3} y^4 $$
$$ \text { (d) }-2 k^5 \times p^6 \times \frac{1}{4} p^5 \times 3 k $$
Penyelesaian:
(a)
$$ \begin{aligned} & 5^4 \times 9^3 \times 5 \times 9^2 \\ & =5^4 \times 5 \times 9^3 \times 9^2 \\ & =5^{4+1} \times 9^{3+2} \\ & =5^5 \times 9^5 \end{aligned} $$
(b)
$$ \begin{aligned} & (0.4)^2 \times(1.2)^3 \times(0.4) \times(1.2)^5 \times(1.2) \\ & =(0.4)^2 \times(0.4) \times(1.2)^3 \times(1.2)^5 \times(1.2) \\ & =(0.4)^{2+1} \times(1.2)^{3+5+1} \\ & =(0.4)^3 \times(1.2)^9 \end{aligned} $$
(c)
$$ \begin{aligned} & 12 x^5 \times y^3 \times \frac{1}{2} x \times \frac{2}{3} y^4 \\ & =\left(12 \times \frac{1}{2} \times \frac{2}{3}\right)\left(x^5 \times x\right)\left(y^3 \times y^4\right) \\ & =4\left(x^{5+1}\right)\left(y^{3+4}\right) \\ & =4 x^6 y^7 \end{aligned} $$
(d)
$$ \begin{aligned} & -2 k^5 \times p^6 \times \frac{1}{4} p^5 \times 3 k \\ & =\left(-2 \times \frac{1}{4} \times 3\right)\left(k^5 \times k\right)\left(p^6 \times p^5\right) \\ & =-\frac{3}{2}\left(k^{5+1}\right)\left(p^{6+5}\right) \\ & =-\frac{3}{2} k^6 p^{11} \end{aligned} $$
Nyatakan dalam bentuk indeks paling ringkas.
$$ \text { (a) } 5^4 \times 9^3 \times 5 \times 9^2 $$
$$ \text { (b) }(0.4)^2 \times(1.2)^3 \times(0.4) \times(1.2)^5 \times(1.2) $$
$$ \text { (c) } 12 x^5 \times y^3 \times \frac{1}{2} x \times \frac{2}{3} y^4 $$
$$ \text { (d) }-2 k^5 \times p^6 \times \frac{1}{4} p^5 \times 3 k $$
Penyelesaian:
(a)
$$ \begin{aligned} & 5^4 \times 9^3 \times 5 \times 9^2 \\ & =5^4 \times 5 \times 9^3 \times 9^2 \\ & =5^{4+1} \times 9^{3+2} \\ & =5^5 \times 9^5 \end{aligned} $$
(b)
$$ \begin{aligned} & (0.4)^2 \times(1.2)^3 \times(0.4) \times(1.2)^5 \times(1.2) \\ & =(0.4)^2 \times(0.4) \times(1.2)^3 \times(1.2)^5 \times(1.2) \\ & =(0.4)^{2+1} \times(1.2)^{3+5+1} \\ & =(0.4)^3 \times(1.2)^9 \end{aligned} $$
(c)
$$ \begin{aligned} & 12 x^5 \times y^3 \times \frac{1}{2} x \times \frac{2}{3} y^4 \\ & =\left(12 \times \frac{1}{2} \times \frac{2}{3}\right)\left(x^5 \times x\right)\left(y^3 \times y^4\right) \\ & =4\left(x^{5+1}\right)\left(y^{3+4}\right) \\ & =4 x^6 y^7 \end{aligned} $$
(d)
$$ \begin{aligned} & -2 k^5 \times p^6 \times \frac{1}{4} p^5 \times 3 k \\ & =\left(-2 \times \frac{1}{4} \times 3\right)\left(k^5 \times k\right)\left(p^6 \times p^5\right) \\ & =-\frac{3}{2}\left(k^{5+1}\right)\left(p^{6+5}\right) \\ & =-\frac{3}{2} k^6 p^{11} \end{aligned} $$