| No. | Law | Formula |
| 1 | Product Rule | $a^m \times a^n = a^{m+n}$ |
| 2 | Quotient Rule | $\frac{a^m}{a^n} = a^{m-n}$ |
| 3 | Power of a Power | $(a^m)^n = a^{mn}$ |
| 4 | Power of a Product | $(ab)^n = a^n b^n$ |
| 5 | Power of a Fraction | $(\frac{a}{b})^n = \frac{a^n}{b^n}$ |
| 6 | Zero Exponent | $a^0 = 1$ |
| No. | Law / Property | Formula |
| 1 | Radical to Exponent | $\sqrt[n]{a} = a^{1/n}$ |
| 2 | Product of Surds | $\sqrt[n]{ab} = \sqrt[n]{a} \times \sqrt[n]{b}$ |
| 3 | Quotient of Surds | $\sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}}$ |
| 4 | Power of a Surd | $(\sqrt[n]{a})^n = a$ |
| 5 | Nested Surds | $\sqrt[m]{\sqrt[n]{a}} = \sqrt[mn]{a}$ |
| 6 | Power inside Surd | $(\sqrt[n]{a})^m = \sqrt[n]{a^m}$ |
