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maryoomsaggaf

Let's break down why (-1)^15 equals -1.

Understanding Negative Exponents:

  • An exponent tells you how many times a number (the base) is multiplied by itself.
  •   For example, 2^3 (2 to the power of 3) means 2 multiplied by itself three times: 2 x 2 x 2.

Even vs. Odd Exponents for Negative Bases:

  • When the base is negative (-1 in this case), the outcome depends on whether the exponent is even or odd.
  • Even Exponents:  Any negative number raised to an even power results in a positive number.

   Example: (-1)^2 = (-1) x (-1) = 1 (positive)

  • Odd Exponents: Any negative number raised to an odd power results in a negative number.

    Example: (-1)^3 = (-1) x (-1) x (-1) = -1 (negative)

Why (-1)^15 is -1:

Since 15 is an odd number (1, 3, 5, etc. are all odd), raising -1 to the power of 15 follows the rule of odd exponents for negative bases. This means:

(-1)^15 = (-1) multiplied by itself 15 times.

Following the pattern of even exponents resulting in positives and odd exponents resulting in negatives, we get:

(-1)^15 = - (positive number) (because -1 multiplied by itself an odd number of times makes a positive)

Therefore, (-1)^15 = -1.

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