Adapted from Wentworth's Elementary Algebra for MathDoctor.net
In Chapter 1, we learned that 3x is a shortcut for adding x three times (x + x + x). An Exponent is a shortcut for multiplying a number by itself several times.
In the expression x3:
x3 = x • x • x
While we can raise a number to any power, the two most common are "Squared" and "Cubed." These names come from Geometry:
Mental Math Check
2 squared (22) = 2 • 2 = 4
2 cubed (23) = 2 • 2 • 2 = 8
2 to the 4th (24) = 2 • 2 • 2 • 2 = 16
Computer science is built on exponents (specifically base 2 and base 10). When you see a "Kilobyte," you are looking at 103 bytes. A "Megabyte" is 106 bytes.
Understanding exponents helps you understand why technology grows so fast. It's not a straight line; it's exponential growth.
Be careful when raising negative numbers to a power. Remember the "Sign Rules" from Chapter 6!
Rule of Thumb: An even exponent results in a positive answer; an odd exponent keeps the negative sign.
Try evaluating these expressions:
Disclosure: This page contains affiliate links; we may earn a commission from qualifying purchases.
Exponents grow incredibly fast. To internalize the scale of powers and square roots, we recommend a Large Print Exponent Poster for your study area. Having these common squares and cubes in your peripheral vision helps you recognize mathematical patterns much faster as you work through Chapter 7.
Reference: image_80c323.png