Laws of indices

There are 7 main laws of indices you need to know. These tell us how to simplify expressions when:

flashcards

Question	Answer
Law of indices: multiplying indices	What happens when you multiply expressions with the same base? Keep the base, add the powers: a^m \times a^n = a^{m+n}
Law of indices: dividing indices	What happens when you divide expressions with the same base? Keep the base, subtract the powers: a^m \div a^n = a^{m-n}
Law of indices: raising an index to an index	What happens when you raise an index to another index? Keep the base, multiply the powers: (a^m)^n = a^{m \times n}
Law of indices: power of 1	What is the value of any expression raised to the power of 1? The expression itself: a^1 = a
Law of indices: power of 0	What is the value of any non-zero expression raised to the power of 0? It equals 1: a^0 = 1 (for a \neq 0)
Law of indices: fractional powers	How do you interpret a fractional power like a^{m/n}? The numerator m is the power, the denominator n is the root: a^{m/n} = \sqrt[n]{a^m} = (\sqrt[n]{a})^m
Law of indices: negative powers	How do you interpret a negative power like a^{-n}? It is the reciprocal: a^{-n} = \frac{1}{a^n} (for a \neq 0)
Number of main laws of indices	How many main laws of indices do you need to know? 7 main laws of indices.
Purpose of laws of indices	What do the laws of indices tell us? How to simplify expressions involving indices (powers).