Mathematics Chapter on Exponents and Notation

Scientific Notation

• Scientific notation expresses very large or very small numbers in a concise way.
• It uses powers of 10 to represent the magnitude of the number.
• Example: 3.2 x 10⁶

Base Ten (Writing Numbers)

• Base ten refers to the decimal system where each place value represents a power of 10.
• Units, tens, hundreds, thousands, and so on all relate to powers of ten.
• Examples are easy to understand with the value of the decimal place positions.

Repeated Multiplication, Base, Exponent, Power, Standard Form

• Repeated multiplication using a base and exponent represent the base raised to the power of the exponent.
• Example: 2³ = 2 x 2 x 2 = 8.

Law of Zero

• Any number raised to the power of zero equals one (except zero to the zero power, which is undefined).
• Example: 5⁰ = 1

Negative Exponents

• A negative exponent indicates the reciprocal of the base raised to the positive exponent.
• Example: 3^-2 = 1/3² = 1/9

Laws of Exponents (Product, Quotient, and Power)

• Product of powers: When multiplying two powers with the same base, add the exponents.
• Example: a^m x aⁿ = a^(m+n)
• Quotient of powers: When dividing two powers with the same base, subtract the exponents.
• Example: a^m / aⁿ = a^(m-n)
• Power of a power: When a power is raised to another power, multiply the exponents.
• Example: (a^m)ⁿ = a^{(m x n)}

Order of Operations (Solving using only Exponent Laws)

• Follow the order of operations, including exponent operations, when solving expressions.

Find the Error in Order of Operations

• This topic likely involves identifying and explaining mistakes in problem-solving steps that violate the order of operations.
• Practice problems are needed to demonstrate how to use exponent laws in solving problems with order of operations.