Bilangan Berpangkat Pecahan

Bentuk-bentuk perpangkatan seperti $ 3^{\frac{1}{3}}, 4^{-\frac{2}{5}}, 5^{\frac{3}{2}}, 6^{\frac{3}{5}}, 8^{-\frac{3}{4}} $ adalah bentuk-bentuk bilangan berpangkat pecahan. Secara umum, bilangan berpangkat pecahan biasa ditulis: $a^{\frac{m}{n}}$ dimana $a$ merupakan bilangan real, $m$ dan $n$ merupakan bilangan asli, serta $a$ dan $n$ tidak sama dengan $0$.

Pangkat Pecahan Bentuk $a^{\frac{1}{n}}$

Perlu kita ketahui bahwa :

Jika $2^{\color{red}{2}} = \color{blue}{4}$, maka $2 = \sqrt[\color{red}{2}]{\color{blue}{4}} $ atau $\sqrt{\color{blue}{4}}$

Jika $3^{\color{red}{3}} = \color{blue}{27}$, maka $3 = \sqrt[\color{red}{3}]{\color{blue}{27}}$

Jika $2^{\color{red}{4}} = \color{blue}{16}$, maka $2 = \sqrt[\color{red}{4}]{\color{blue}{16}}$

Jika $2^{\color{red}{5}} = \color{blue}{32}$, maka $2 = \sqrt[\color{red}{5}]{\color{blue}{32}}$

Jika $b^{\color{red}{6}} = \color{blue}{a}$, maka $b = \sqrt[\color{red}{6}]{\color{blue}{a}}$

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Perhatikan operasi berikut:

$2^{2} = 4$	$2 = $ $\sqrt{4}$	$2^{2} = 4 $ $(2^{2})^{\frac{1}{2}} = 4^{\frac{1}{2}}$ $2^{\frac{2}{2}} = 4^{\frac{1}{2}}$ $2^{1} = 4^{\frac{1}{2}}$ $2 = $$4^{\frac{1}{2}}$
	Maka, $ \sqrt{4}$ $ = $ $4^{\frac{1}{2}} $
$3^{3} = 27$	$3 = $$\sqrt[3]{27}$	$3^{3} = 27 $ $(3^{3})^{\frac{1}{3}} = 27^{\frac{1}{3}}$ $3^{\frac{3}{3}} = 27^{\frac{1}{3}}$ $3^{1} = 27^{\frac{1}{3}}$ $3 = $$27^{\frac{1}{3}}$
	Maka, $\sqrt[3]{27} $$ = $$27^{\frac{1}{3}} $
$2^{4} = 16$	$2 = $$\sqrt[4]{16}$	$2^{4} = 16 $ $(2^{4})^{\frac{1}{4}} = 16^{\frac{1}{4}}$ $2^{\frac{4}{4}} = 16^{\frac{1}{4}}$ $2^{1} = 16^{\frac{1}{4}}$ $2 = $$16^{\frac{1}{4}}$
	Maka, $ \sqrt[4]{16}$$ = $$16^{\frac{1}{4}} $
$2^{5} = 32$	$2 = $$\sqrt[5]{32}$	$2^{5} = 32 $ $(2^{5})^{\frac{1}{5}} = 32^{\frac{1}{5}}$ $2^{\frac{5}{5}} = 32^{\frac{1}{5}}$ $2^{1} = 32^{\frac{1}{5}}$ $2 = $$32^{\frac{1}{5}}$
	Maka, $ \sqrt[5]{32}$$ = $$32^{\frac{1}{5}} $