Skill: Evaluate whole-number powers

Explanation and Free Practice Resources

A whole-number power ana^n represents a product of nn equal factors of the whole-number base aa; the base identifies the repeated factor, and the exponent identifies how many factors occur. Evaluation includes numerical powers with nonnegative integer exponents, including the convention a0=1a^0=1 for nonzero aa, and distinguishes exponentiation from multiplying the base by the exponent. Negative or fractional exponents and generalized exponent laws are not included.

Detailed Explanation: Evaluate whole-number powers

A power shows repeated multiplication.

In ana^n:

  • aa is the base, or the factor being repeated.
  • nn is the exponent, or the number of times the base is used as a factor.

Example: Evaluate 343^4

  1. The base is 33, and the exponent is 44.
  2. Write 33 as a factor four times:
34=3⋅3⋅3⋅33^4=3\cdot3\cdot3\cdot3
  1. Multiply:
3⋅3=9,9⋅3=27,27⋅3=813\cdot3=9,\qquad 9\cdot3=27,\qquad 27\cdot3=81
  1. Therefore:
34=81\boxed{3^4=81}

Remember, 343^4 means 3⋅3⋅3⋅33\cdot3\cdot3\cdot3, not 3⋅43\cdot4. For any nonzero whole number aa, a0=1a^0=1.

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