Bab 5 Indeks dan Logaritma

(C) Indeks Pecahan
$$\boxed{\begin{array}{l}\text{ Secara amnya, bagi semua }a.\\ a^{\frac{1}{n}}=\sqrt[n]{a}\\ a^{\frac{m}{n}}=\sqrt[n]{a^m}={\left(\sqrt[n]{a}\right)}^m\\ \ast \sqrt[n]{a}\text{ disebut punca kuasa }n\text{ bagi }a.\\ \ast {\left(\sqrt[n]{a}\right)}^m\text{disebut kuasa }m\text{ bagi }\\ \text{ punca kuasa }n\text{ bagi }a.\end{array}}$$

$\boxed{\begin{array}{l}{a}^m\times a^n=a^{m+n}\\ \\ \text{ Contoh:}\\ 3^3\times 3^2\\ =3^{3+2}=3^5=243\end{array}}$

$\boxed{\begin{array}{l}{a}^m÷a^n=a^{m-n}\text{ atau }\frac{a^m}{a^n}=a^{m-n},a\ne 0\\ \\ \text{ Contoh:}\\ 3^3÷3^2\\ =3^{3-2}=3^1=3\\ \text{ atau}\\ \frac{3^3}{3^2}=3^{3-2}=3^1=3\end{array}}$

$\boxed{\begin{array}{l}{\left(a^m\right)}^n=a^{mn}\\ \\ \text{ Contoh:}\\ {\left(7^3\right)}^4=7^{3\times 4}=7^{12}\end{array}}$

$\boxed{\begin{array}{l}{\left(ab\right)}^n=a^n{b}^n\\ \\ \text{ Contoh:}\\ {\left(15\right)}^3={\left(5\times 3\right)}^3=2^3\times 3^3\\ \end{array}}$

$\boxed{\begin{array}{l}{\left(\frac{a}{b}\right)}^n=\frac{a^n}{b^n},b\ne 0\\ \\ \text{ Contoh:}\\ {\left(\frac{3}{5}\right)}^4=\frac{3^4}{5^4}=\frac{81}{625}\end{array}}$