Exponents with a negative base

  • If we are working with a negative number raised to a power, the base does not include the negative part unless we use parentheses
    • -2 ≠ (-2)
    • -2 = -(2)
  • -2 is the same as -1 x 2  so from the order of operations...
    • -2 = -1 x 2 = -1 x 4 = -4
  • (-2) has the negative in the base
    • (-2) = (1 x -2) = -2 x -2 = 4

Sign rules for evaluating an exponent with a negative base

  • When the base is (-), and enclosed inside of parentheses:
    • The result is (+) if the exponent is even
    • The result is (-) if the exponent is odd
  • When the base is (-), and not enclosed inside of parentheses:
    • The result is always (-)
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Exponents with a negative base
Sign rules for evaluating an exponent with a negative base