Key vocabulary for Expressions, Equations, and Exponents.
The set of all rational and irrational numbers.
Natural: \(\{1, 2, 3, ...\}\)
Whole: \(\{0, 1, 2, 3, ...\}\)
Integers: \(\{..., -2, -1, 0, 1, 2, ...\}\)
Rational: Numbers that can be a fraction, like \(\frac{1}{2}, -3, 0.25\).
Irrational: Numbers that can't be a fraction, like \(\pi, \sqrt{2}\).
A number's distance from zero on the number line. Distance is always positive.
\(\lvert-5\rvert = 5\)
\(\lvert5\rvert = 5\)
The rules that state the sequence in which the multiple operations in an expression should be solved.
1. Parentheses (or Grouping Symbols)
2. Exponents
3. Multiplication & Division (Left to Right)
4. Addition & Subtraction (Left to Right)
A mathematical phrase that can contain numbers, variables, and operators. It does not have an equal sign.
\(3x^2 + 2y - 5\)
A symbol, usually a letter, that represents an unknown value.
In \(9 + x = 15\), the variable is \(x\).
The number multiplied by a variable in a term.
In the term \(-4x\), the coefficient is \(-4\).
A single number, a variable, or numbers and variables multiplied together. Terms are separated by + or - signs.
The expression \(5x - 2y + 8\) has 3 terms.
A way of writing repeated multiplication using a base and an exponent.
\(2 \cdot 2 \cdot 2 = 2^3\)
Base: 2, Exponent: 3
Rules for simplifying expressions with exponents.
Product: \(a^m \cdot a^n = a^{m+n}\)
Power of Power: \((a^m)^n = a^{mn}\)
Power of Product: \((ab)^m = a^m b^m\)
Quotient: \(\frac{a^m}{a^n} = a^{m-n}\)
Power of Quotient: \((\frac{a}{b})^m = \frac{a^m}{b^m}\)
Zero Exponent: \(a^0 = 1\)
Negative Exponent: \(a^{-n} = \frac{1}{a^n}\)