Laws of Exponents

Flashcards covering the laws of exponents.

Laws of Exponents

Rules that explain how to handle mathematical operations involving powers of numbers. Exponents are used to represent numbers that are multiplied by themselves a certain number of times.

Exponent

A small number written in the upper-right corner of the base number, indicating how many times the base number has been multiplied by itself.

Product of Powers

When you multiply two numbers with the same base, you add their exponents: a^m × a^n = a^(m+n)

Quotient of Powers

When you divide two numbers with the same base, you subtract the exponent of the denominator from the exponent of the numerator: a^m ÷ a^n = a^(m-n)

Power of a Power

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

Power of a Product

When you raise a product to an exponent, it applies to each of the factors: (a × b)^n = a^n × b^n

Power of a Quotient

If the quotient is raised to an exponent, then the exponent applies to both the numerator and the denominator: (a ÷ b)^n = a^n ÷ b^n

Zero Exponent

The power of a nonzero base is zero: a^0 = 1 (where a ≠ 0)

Negative Exponent

A negative exponent means you take the inverse of the base: a^(-n) = 1/a^n