Factsheet: Laws of indices
The associated study guide for this factsheet is Guide: Laws of indices. If you would like to know more about these, please read the guide.
Throughout this factsheet, \(a, b\) are positive real numbers, \(r\) and \(s\) are real numbers, and \(n\) is a positive whole number.
Laws of indices
Law 1: \(\quad a^r·a^s = a^{r+s}\).
Law 2: \(\quad\dfrac{a^r}{a^s} = a^{r-s}\).
Law 3: \(\quad(a^r)^s = a^{r·s}\).
Law 4: If \(a\) is non-zero, then \(a^0 = 1\).
Law 5: \(\quad a^{-r} = \dfrac{1}{a^r}\)
Law 6: \(\quad\displaystyle a^{1/n} = \sqrt[n]{a}.\)
Law 7: \(\quad a^r \cdot b^r = (ab)^r\).
Law 8: \(\quad\dfrac{a^r}{b^r} = \left(\dfrac{a}{b}\right)^r\).
Law 9: \(\displaystyle \quad a^{1/n} \cdot b=\sqrt[n]{a \cdot b^n}\).
Law 10: \(\displaystyle\quad\sqrt[n]{a\cdot b}=\sqrt[n]{a}\cdot\sqrt[n]{b}\).
For more on the subject, please go to Guide: Laws of indices
Version history
v1.0: created in 05/24 by tdhc.