Powers & Exponents

Vocabulary flashcards covering key exponent rules and monomial concepts from the notes.

Exponent

A number that indicates how many times the base is used as a factor in multiplication (as in a^n).

Product Rule for Exponents

When multiplying like bases, add the exponents: a^m · a^n = a^(m+n).

Quotient Rule for Exponents

When dividing like bases, subtract the exponents: a^m / a^n = a^(m-n).

Zero Exponent Rule

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

Power of a Power Rule

Raise a power to another power by multiplying exponents: (a^m)^n = a^(m·n).

Power of a Product Rule

Distribute the exponent over a product: (ab)^n = a^n b^n.

Power of a Quotient Rule

Raise a fraction to a power: (a/b)^n = a^n / b^n.

Negative Exponent Rule

A negative exponent indicates a reciprocal: a^(-n) = 1 / a^n (a ≠ 0).

Monomial

A single term, such as 3x^2y; consists of a coefficient and variables with nonnegative integer exponents.

Even vs Odd Exponent Sign Rule

If the base is negative, the sign depends on parity: even exponents yield a positive result, odd exponents yield a negative result.