1. What are Exponents?

• An exponent refers to the number of times a number (called the base) is multiplied by itself.
• It is written in the form: a^n, where:
  • a is the base.
  • n is the exponent (or power).

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2. Basic Terminology

• Base: The number being multiplied.
• Exponent: The number showing how many times the base is used as a factor.
• Example: In 3^4, 3 is the base, and 4 is the exponent. This means 3 × 3 × 3 × 3 = 81.

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3. Understanding Powers of 10

• Exponents are commonly used with the base 10 to represent large or small numbers.
• Example: 10^3 = 10 × 10 × 10 = 1000.

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4. Exponent Rules

• Product Rule: When multiplying two numbers with the same base, add the exponents.
  • Example: a^m × a^n = a^(m+n).
  • Example: 2^3 × 2^2 = 2^(3+2) = 2^5 = 32.
• Quotient Rule: When dividing two numbers with the same base, subtract the exponents.
  • Example: a^m ÷ a^n = a^(m−n).
  • Example: 5^6 ÷ 5^2 = 5^(6-2) = 5^4 = 625.
• Power Rule: When raising an exponent to another exponent, multiply the exponents.
  • Example: (a^m)^n = a^(m×n).
  • Example: (2^3)^2 = 2^(3×2) = 2^6 = 64.
• Zero Exponent Rule: Any non-zero number raised to the power of 0 is equal to 1.
  • Example: a^0 = 1 (if a ≠ 0).
• Negative Exponent Rule: A number with a negative exponent represents the reciprocal of the number raised to the positive exponent.
  • Example: a^(-n) = 1/a^n.
  • Example: 2^(-3) = 1/2^3 = 1/8.

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5. Working with Large and Small Numbers

Exponents make it easier to express large or small numbers in scientific notation.

Example: 3 × 10^6 represents 3,000,000.