Final answer:
The base (4) in the expression 4 to the third power (4³) is multiplied by itself as many times as the exponent (3) indicates, yielding 4 x 4 x 4 = 64.
Step-by-step explanation:
The relationship between the base and the exponent in an expression like 4 to the third power (4³) involves repeated multiplication. The base, which is 4 in this case, is the number that we multiply by itself. The exponent, which is 3, indicates the number of times the base is multiplied. Therefore, 4³ means 4 multiplied by itself three times, which would be:
4 x 4 x 4 = 64
This type of operation where we use an exponent is a form of mathematical shorthand, significantly simplifying the representation of large numbers that result from such repeated multiplication.