Laws of Indices Flashcards

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

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

When raising a power to another power, multiply the indices: (a^m)^n = a^(m×n).

Any number raised to the power of 0 is equal to 1: a^0 = 1 (where a ≠ 0).

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

A fractional index represents a root: a^(1/n) = n√a (the nth root of a).

A fractional index combines a power and a root: a^(m/n) = (n√a)^m or n√(a^m).

Indices rules only apply when the base is the same (e.g., a^m × a^n).

Combine terms using the laws of indices, ensuring the base is the same.

Add the indices: 2^3 × 2^4 = 2^(3+4) = 2^7.