Algebra 1

Monomial

An algebraic expression consisting of a single term formed by a number, a variable, or the product of numbers and variables with nonnegative integer exponents.

Degree of a monomial

The sum of the exponents of all the variables present in a single algebraic term.

Quotient of Powers Property

A mathematical rule stating that when dividing powers with the same nonzero base, the exponent of the denominator is subtracted from the exponent of the numerator: $\frac{a^m}{a^n} = a^{m-n}$, where $a \neq 0$.

Power of a Quotient Property

A mathematical rule stating that to raise a fraction to an exponent, apply the exponent to both the numerator and the denominator separately: $(\frac{a}{b})^m = \frac{a^m}{b^m}$, where $b \neq 0$.

Negative Exponent Rule

A rule stating that any nonzero base raised to a negative power equals the reciprocal of the base raised to the corresponding positive power: $a^{-n} = \frac{1}{a^n}$ and $\frac{1}{a^{-n}} = a^n$, where $a \neq 0$.

Rational exponent with a unit fraction ($a^{\frac{1}{n}}$)

An algebraic expression where a fractional exponent represents the principal $n$-th root of the base: $a^{\frac{1}{n}} = \sqrt[n]{a}$, where $n$ is a positive integer.

General rational exponent ($a^{\frac{m}{n}}$)

An expression where the denominator represents the index of the radical and the numerator represents the power: $a^{\frac{m}{n}} = \sqrt[n]{a^m} = (\sqrt[n]{a})^m$, where $m$ and $n$ are integers and $n > 0$.

Zero Exponent Property

A property stating that any nonzero base raised to the power of zero equals one: $a^0 = 1$, where $a \neq 0$.