Index Laws & Scientific Notation - Vocabulary Flashcards

Vocabulary terms from the lecture notes on index laws and scientific notation.

Exponent (Index)

The power to which the base is raised; in a^m, m is the exponent.

Base

The number or symbol being raised to a power in a^m; the base is a.

Positive index

An exponent that is a positive integer.

Zero index

Any nonzero number raised to the power 0 equals 1 (a^0 = 1 for a ≠ 0).

Negative index

An exponent that is negative; a^(-n) = 1 / a^n.

Product rule (same base)

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

Quotient rule (same base)

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

Power of a power

(a^m)^n = a^(mn).

Brackets rule (power of a product)

(ab)^m = a^m b^m.

Surd

An irrational root that cannot be expressed as a rational number; e.g., √2.

Like surds

Surds with the same radicand that can be added or subtracted.

Radical multiplication

√a × √b = √(ab) (when a,b ≥ 0).

Fractional indices

Exponents like a^(1/n) mean the nth root of a; more generally a^(m/n) = (a^m)^(1/n).

Index form

Writing a number using a base raised to a power, e.g., 2^5.

Scientific notation

Writing numbers as a × 10^n where 1 ≤ |a| < 10; large numbers use positive n, small numbers use negative n.

Significant figures

Digits that contribute to a number’s precision; used when rounding to a specified number of significant figures.

Large numbers (in scientific notation)

Numbers with positive exponent in scientific notation, e.g., 2.35 × 10^6.

Small numbers (in scientific notation)

Numbers with negative exponent in scientific notation, e.g., 1.6 × 10^-8.