#### Quotient rules of exponents

Let $m$ and $n$ be positive integers and let $a$ represent a real number, a variable, or an algebraic expression.

1. \(\frac{{{a^m}}}{{{a^n}}} = {a^{m – n}}\), \(m > n\), \(a \ne 0\).

2. \(\frac{{{a^n}}}{{{a^n}}} = 1 = {a^0}\), \(a \ne 0\).

#### Quotient rule for radicals

Let $a$ and $b$ be real numbers, variables, or algebraic expressions. If the $n$th roots of $a$ and $b$ are real, then the following property is true. \(\sqrt[n]{{\frac{a}{b}}} = \frac{{\sqrt[n]{a}}}{{\sqrt[n]{b}}}\), \(b \ne 0\).

#### Quotient

The result of dividing one term by another.

#### Quadratic formula

The solutions of \(a{x^2} + bx + c = 0\), \(a \ne 0\), are given by \(x = \frac{{ – b \pm \sqrt {{b^2} – 4ac} }}{{2a}}\).

#### Quadratic equation

An equation that can be written in the general form \(a{x^2} + bx + c = 0\) where $a$, $b$, and $c$ are real numbers with \(a \ne 0\).

#### Quadrants

The four regions the $x$- and $y$-axes separate the plane of a rectangular coordinate system into.