Uji Minda 1.2b – Buku Teks Matematik Tingkatan 3 Bab 1 (Indeks)

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)
$$
\begin{aligned}
& -2 k^5 \times p^6 \times \frac{1}{4} p^5 \times 3 k \\
& =\left(-2 \times \frac{1}{4} \times 3\right)\left(k^5 \times k\right)\left(p^6 \times p^5\right) \\
& =-\frac{3}{2}\left(k^{5+1}\right)\left(p^{6+5}\right) \\
& =-\frac{3}{2} k^6 p^{11}
\end{aligned}
$$