Integer exponents and scientific notation

Develop control of integer powers and scientific notation, two forms of notation used throughout precalculus and quantitative science. This set covers products and quotients of powers, powers of products, zero and negative exponents, signs of negative bases and the role of parentheses. Nonzero-base conditions are stated where division or reciprocals require them.

Scientific-notation questions move from reading and normalizing numbers to multiplication, division, addition, comparison and scale factors. You will distinguish a numerically equivalent expression from one written in the requested normalized form and check whether a negative exponent changes magnitude or sign. Later tasks combine several rules, examine an invalid extension of a rule, and connect powers to geometric scaling.

Use the meaning of an exponent to justify each transformation before compressing it into a rule. Both single-answer and select-all questions are included, with explanations that show the calculation and identify the limits of the method. Familiarity with substitution, distribution and fraction arithmetic is helpful. Rational exponents and radical rules come next; the present set establishes the integer-power foundations without relying on logarithms.