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Exponents definitions

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  • Exponent
    A small number written above and to the right of a base, indicating how many times the base is multiplied by itself.
  • Base
    The number or variable that is repeatedly multiplied in an exponential expression.
  • Product Rule
    A rule stating that when multiplying like bases, their exponents are added together.
  • Quotient Rule
    A rule stating that when dividing like bases, their exponents are subtracted.
  • Power Rule
    A rule stating that when raising a power to another power, the exponents are multiplied.
  • Power of a Product Rule
    A rule stating that an exponent outside parentheses distributes to each factor inside.
  • Power of a Quotient Rule
    A rule stating that an exponent outside parentheses distributes to both the numerator and denominator.
  • Zero Exponent Rule
    A rule stating that any nonzero base raised to the zero power equals one.
  • Negative Exponent Rule
    A rule stating that a negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent.
  • Like Terms
    Terms that have identical variable parts and exponents, allowing them to be combined.
  • Reciprocal
    A value obtained by inverting a fraction or flipping a base with a negative exponent to the opposite side of a fraction.
  • Parentheses
    Symbols used to group terms, indicating that operations inside should be performed first or that exponents apply to the entire group.
  • Simplification Checklist
    A step-by-step process to ensure all exponent rules are applied and the expression is fully simplified.
  • Order of Operations
    A sequence dictating the correct order to evaluate expressions, often remembered as PEMDAS.
  • Distributive Property
    A property allowing an exponent or multiplication to be applied to each term within parentheses.