Evaluate whole-number powers

A whole-number power $a^n$ represents a product of $n$ equal factors of the whole-number base $a$ ; 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 $a^0=1$ for nonzero $a$ , 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 $a^n$ :

$a$ is the base, or the factor being repeated.
$n$ is the exponent, or the number of times the base is used as a factor.

Example: Evaluate $3^4$

The base is $3$ , and the exponent is $4$ .
Write $3$ as a factor four times:

3^4=3\cdot3\cdot3\cdot3

Multiply:

3\cdot3=9,\qquad 9\cdot3=27,\qquad 27\cdot3=81

Therefore:

\boxed{3^4=81}

Remember, $3^4$ means $3\cdot3\cdot3\cdot3$ , not $3\cdot4$ . For any nonzero whole number $a$ , $a^0=1$ .

Learn by doing: Evaluate whole-number powers

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Exponents Concept Intro - Power to Number - Exponents to Three

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