Index Notation Flashcards

A way of writing numbers using powers or exponents, e.g., 2³ means 2 × 2 × 2.

The number that is being multiplied in index notation, e.g., in 2³, the base is 2.

The small number written above and to the right of the base, showing how many times the base is multiplied by itself.

When multiplying powers with the same base, add the exponents: aᵐ × aⁿ = aᵐ⁺ⁿ.

When dividing powers with the same base, subtract the exponents: aᵐ ÷ aⁿ = aᵐ⁻ⁿ.

When raising a power to another power, multiply the exponents: (aᵐ)ⁿ = aᵐⁿ.

Any number raised to the power of 0 is equal to 1: a⁰ = 1 (where a ≠ 0).

A negative exponent means the reciprocal of the base raised to the positive exponent: a⁻ⁿ = 1/aⁿ.

A fractional exponent represents a root: a^(1/n) = n√a, and a^(m/n) = (n√a)ᵐ.

Standard form uses powers of 10 to express very large or small numbers, e.g., 3 × 10⁴ = 30000.