Soalan 1:
Hitung nilai setiap yang berikut.
Penyelesaian:
(a)
$$ 27^{\frac{2}{3}}=(\sqrt[3]{27})^2=(3)^2=9 $$
(b)
$$ 32^{\frac{2}{5}}=(\sqrt[5]{32})^2=(2)^2=4 $$
(c)
(d)
(e)
$$ 64^{\frac{4}{3}}=\left(4^3\right)^{\frac{4}{3}}=(4)^4=256 $$
(f)
$$ 1024^{\frac{2}{5}}=\left(4^5\right)^{\frac{2}{8}}=(4)^2=16 $$
(g)
$$ 1296^{\frac{3}{4}}=\left(6^4\right)^{\frac{3}{4}}=(6)^3=216 $$
(h)
$$ 49^{\frac{3}{2}}=\left(7^2\right)^{\frac{3}{2}}=(7)^3=343 $$
(i)
$$ 2401^{\frac{1}{4}}=\left(7^4\right)^{\frac{1}{\frac{4}{4}}}=(7)^1=7 $$
(j)
$$ 121^{\frac{3}{2}}=\left(11^2\right)^{\frac{3}{2}}=(11)^3=1331 $$
(k)
$$ 2197^{\frac{2}{3}}=\left(13^3\right)^{\frac{2}{3}}=(13)^2=169 $$
(l)
$$ 10000^{\frac{3}{4}}=\left(10^4\right)^{\frac{3}{4}}=(10)^3=1000 $$
Hitung nilai setiap yang berikut.
Penyelesaian:
(a)
$$ 27^{\frac{2}{3}}=(\sqrt[3]{27})^2=(3)^2=9 $$
(b)
$$ 32^{\frac{2}{5}}=(\sqrt[5]{32})^2=(2)^2=4 $$
(c)
(d)
(e)
$$ 64^{\frac{4}{3}}=\left(4^3\right)^{\frac{4}{3}}=(4)^4=256 $$
(f)
$$ 1024^{\frac{2}{5}}=\left(4^5\right)^{\frac{2}{8}}=(4)^2=16 $$
(g)
$$ 1296^{\frac{3}{4}}=\left(6^4\right)^{\frac{3}{4}}=(6)^3=216 $$
(h)
$$ 49^{\frac{3}{2}}=\left(7^2\right)^{\frac{3}{2}}=(7)^3=343 $$
(i)
$$ 2401^{\frac{1}{4}}=\left(7^4\right)^{\frac{1}{\frac{4}{4}}}=(7)^1=7 $$
(j)
$$ 121^{\frac{3}{2}}=\left(11^2\right)^{\frac{3}{2}}=(11)^3=1331 $$
(k)
$$ 2197^{\frac{2}{3}}=\left(13^3\right)^{\frac{2}{3}}=(13)^2=169 $$
(l)
$$ 10000^{\frac{3}{4}}=\left(10^4\right)^{\frac{3}{4}}=(10)^3=1000 $$