**Equations and Inequalities**

**Rules for Equality: **For all real numbers a, b, and c, if a = b, then the
following rules are valid.

**Rules for Equality: **For all real numbers a, b, and c, if a = b, then the
following rules are valid.

**A polynomial is an expression involving constants, variables
with natural number exponents, the four basic operations of +, -, . and / and no
variables in denominators.**

**Rules for Addition and Subtraction of Polynomials**

- Two terms cannot be added (or subtracted) unless they consist of the...

**When evaluating mathematical expressions we follow this order of operations:**

- Parentheses (from the inside out)
- Exponents (from right to left)
- Multiplication and division (from left to right)
- Addition and subtraction (from left to right)

**Example:**

**Evaluate the expression: **$$\eqalign{
& {{2 \times...

**Rules of Exponentiation: For real numbers a and b and natural numbers m and n:**

$${{\rm{a}}^{\rm{m}}} \times {\rm{ }}{{\rm{a}}^{\rm{n}}}{\rm{ = }}{{\rm{a}}^{{\rm{m + n}}}}$$

$${{{a^m}} \over {{a^n}}} = {a^{m - n}}$$

$${\left( {{a^m}} \right)^n} = {a^{mn}}$$

$${\left( {ab} \right)^n} = {a^n}{b^n}$$

$${\left( {{a \over b}} \right)^n} = {{{a^n}} \over {{b^n}}}$$

...
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