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

Soalan 1:


Penyelesaian:
$$
\begin{aligned}
&\begin{aligned}
& \sqrt[2]{x}=x^{\frac{1}{2}} \\
& \sqrt[3]{x}=x^{\frac{1}{3}}
\end{aligned}\\
&\text { Secara generalisasi, }\\
&\sqrt[n]{a}=a^{\frac{1}{n}} ; a \neq 0
\end{aligned}
$$
(a)
$$
\sqrt[3]{125}=125^{\frac{1}{3}}
$$

(b)
$$
\sqrt[7]{2187}=2187^{\frac{1}{7}}
$$
(c)
$$
\sqrt[5]{-1024}=(-1024)^{\frac{1}{5}}
$$
(d)
$$
\sqrt[10]{n}=n^{\frac{1}{10}}
$$

Soalan 2:

Penyelesaian:
(a)
$$
4^{\frac{1}{2}}=\sqrt{4}
$$
(b)
$$
32^{\frac{1}{5}}=\sqrt[5]{32}
$$
(c)
$$
(-729)^{\frac{1}{3}}=\sqrt[3]{-729}
$$
(d)
$$
n^{\frac{1}{15}}=\sqrt[15]{n}
$$

Soalan 3:

Penyelesaian:
(a)
$$
\begin{aligned}
\sqrt[3]{343} & =343^{\frac{1}{3}} \\
& =\left(7^3\right)^{\frac{1}{3}} \\
& =7^{\frac{3}{3}} \\
& =7^1 \\
& =7
\end{aligned}
$$

(b)
$$
\begin{aligned}
\sqrt[5]{-7776} & =(-7776)^{\frac{1}{5}} \\
& =\left[(-6)^5\right]^{\frac{1}{5}} \\
& =(-6)^{\frac{5}{5}} \\
& =(-6)^1 \\
& =-6
\end{aligned}
$$

(c)
$$
\begin{aligned}
262144^{\frac{1}{6}} & =\left(8^6\right)^{\frac{1}{6}} \\
& =8^{\frac{6}{6}} \\
& =8^1 \\
& =8
\end{aligned}
$$

(d)
$$
\begin{aligned}
(-32768)^{\frac{1}{5}} & =\left[(-8)^5\right]^{\frac{1}{5}} \\
& =(-8)^{\frac{5}{5}} \\
& =(-8)^1 \\
& =-8
\end{aligned}
$$