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Evaluate powers with whole-number bases

Powers represent repeated multiplication: the base is the factor being multiplied, and the whole-number exponent indicates how many factors occur, so expressions such as 434^3 are evaluated as 4×4×4=644 \times 4 \times 4=64. This understanding includes powers of 10 and the convention a0=1a^0=1 for nonzero whole-number aa, while distinguishing the base from the exponent; negative or fractional exponents and other more advanced extensions are not included.

Detailed Explanation: Evaluate powers with whole-number bases

A power shows repeated multiplication.

In 434^3:

  • 44 is the base, so it is the factor being multiplied.
  • 33 is the exponent, so there are three factors of 44.

To evaluate 434^3:

43=4×4×44^3=4\times4\times4

Multiply from left to right:

4×4=164\times4=16 16×4=6416\times4=64

Therefore,

43=64\boxed{4^3=64}

Remember: the exponent tells how many times the base appears as a factor. Also, for any nonzero whole number aa, a0=1a^0=1.

Learn by doing: Evaluate powers with whole-number bases

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