Unit 1
The rules of arithmetic, restated so they still hold once letters replace numbers. Exponent rules and order of operations do most of the work here and are assumed silently by every later unit.
Lesson 1.1
Evaluate powers before multiplication and division, then addition and subtraction. Operations at the same level are evaluated from left to right. Parentheses can make a negative number the base of a power; without them, an initial minus sign is applied after exponentiation.
Lesson 1.2
Multiplying powers with the same base adds exponents; dividing subtracts them. A power of a power multiplies exponents. A negative exponent represents a reciprocal, so the base must be nonzero. These rules do not combine unlike bases by adding their exponents.
Lesson 1.3
A rational number is a ratio of integers with a nonzero denominator. Its decimal expansion terminates or repeats. An irrational number cannot be written as such a ratio. A square root is rational when the radicand is a perfect square rational number; simplify before classifying.
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