Exponentiation
When it is a positive integer, the exponent indicates how many copies of the base are multiplied together. For example, . The base appears times in the repeated multiplication, because the exponent is . Here, is the "base", is the "exponent", and is the "power" or, more specifically, "3 raised to the 5th power".
Mathematics and the Imagination
Chapter 3 is "Pie (, i, e) Transcendental and Imaginary". To motivate e (mathematical constant), they discuss first compound interest and then continuous compounding. "No other mathematical constant, not even , is more closely connected with human affairs" (p 86).
"[e] has played an integral part in helping mathematicians describe and predict what is for man the most important of all natural phenomena – that of growth."
The exponential function, "y" = e ... "is the only function of "x" with the rate of change with respect to "x" equal to the function itself." (p 87) 
The authors define the Gauss plane and describe the action of multiplication by i as rotation through 90°. They address Euler's identity, i.e. the expression "e" + 1 = 0, indicating that the venerable Benjamin Peirce called it "absolutely paradoxical".
A note of idealism is then expressed: "When there is so much humility and so much vision everywhere, society will be governed by science and not its clever people." (pp 103,4)