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)
$$ \sqrt[10]{n}=n^{\frac{1}{10}} $$
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)
$$ n^{\frac{1}{15}}=\sqrt[15]{n} $$
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)
$$ \begin{aligned} (-32768)^{\frac{1}{5}} & =\left[(-8)^5\right]^{\frac{1}{5}} \\ & =(-8)^{\frac{5}{5}} \\ & =(-8)^1 \\ & =-8 \end{aligned} $$
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)
$$ \begin{aligned} (-32768)^{\frac{1}{5}} & =\left[(-8)^5\right]^{\frac{1}{5}} \\ & =(-8)^{\frac{5}{5}} \\ & =(-8)^1 \\ & =-8 \end{aligned} $$