Indices

If m is a positive integer

If m is a positive integer, then a × a × a × ... (m times) = a^m, where 'a' is the base and 'm' is the index or exponent. For example, 2 × 2 × 2 × 2 =

When multiplying powers with the same

When multiplying powers with the same base, add the indices: a^m × a^n = a^(m+n). Example: 2^3 × 2^5 = 2^8.

When dividing powers with the same

When dividing powers with the same base, subtract the indices: a^m ÷ a^n = a^(m-n). Example: 5^7 ÷ 5^3 = 5^4.

When raising a power to another

When raising a power to another power, multiply the indices: (a^m)^n = a^(mn). Example: (3^2)^4 = 3^8.

A negative index represents the reciprocal

A negative index represents the reciprocal: a^(-n) = 1/a^n. Example: 2^(-3) = 1/2^3 = 1/8.