$$\boxed{\begin{array}{l}\text{ Hukum 1:}\\ {\text{ log}}_{a}xy={\text{log}}_{a}x+{\text{log}}_{a}y\\ \\ \text{ Contoh:}\\ {\log }_{5}25x={\text{log}}_{5}25+{\text{log}}_{5}x\\ \\ \text{ Berhati-hati!!}\\ {\text{ log}}_{a}x+{\text{log}}_{a}y\ne {\text{log}}_a\left(x+y\right)\end{array}}$$
$$\boxed{\begin{array}{l}\text{ Hukum 2:}\\ {\text{ log}}_a\left(\frac{x}{y}\right)={\text{log}}_{a}x-{\text{log}}_{a}y\\ \\ \text{ Contoh:}\\ {\log }_5\frac{x}{25}={\text{log}}_{5}x-{\text{log}}_{5}25\\ \\ \text{ Berhati-hati!!}\\ {\text{ log}}_a\frac{x}{y}\ne \frac{{\text{log}}_{a}x}{{\text{log}}_{a}y}\end{array}}$$
$$\boxed{\begin{array}{l}\text{ Hukum 3:}\\ {\text{ log}}_a{x}^m=m{\text{log}}_{a}x\\ \\ \text{ Contoh:}\\ {\log }_5{y}^5=5{\text{log}}_{5}y\\ \\ \text{ Berhati-hati!!}\\ {\left({\text{log}}_{a}x\right)}^2\ne 2{\text{log}}_{a}x\end{array}}$$

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

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

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

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

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

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

Penyelesaian:
$\begin{array}{l}\text{(a) }{102}^{-1}=\frac{1}{102}\\ \text{(b) }-6^{-3}=\frac{1}{-6^3}=-\frac{1}{216}\\ \text{(c) }{\left(\frac{1}{3}\right)}^{-4}={\left(3\right)}^4=81\\ \text{(d) }{\left(\frac{2}{5}\right)}^{-2}={\left(\frac{5}{2}\right)}^2=\frac{25}{4}\\ \text{(e) }{\left(-\frac{2}{5}\right)}^{-4}={\left(-\frac{5}{2}\right)}^4=\frac{625}{16}\end{array}$