Roots and Exponents

Fundamentals of Social Statistics by Adam J. McKee

In statistics, there is a lot of squaring.  To square a number, simply multiply the number by itself.

Example: 32 = 3 x 3 = 9

Note that we know to multiply 3 by itself in the above example because the raised up number 2—the exponent—tells us to multiply the number preceding the exponent by itself that number of times. This can also be expressed as “three to the second power.”

We can raise a number to the third power, called cubing.

Example:  23 = 2 x 2 x 2 = 8

Special Exponent Rules

-Any number raised to the first power equals itself.

-If any exponent appears outside of parentheses, then any operations inside the parentheses are done first.

-If a negative number is raised to an exponent, the result will be positive for exponents that are even and negative for exponents that are odd.

-An exponent applies only to the base that is just in front of it.

A number printed above the line like an exponent is called a superscript.  This is the term to look for when formatting an exponent on your computer.

Taking a square root is the opposite of squaring.  This means, for example, that the square root of 9 is 3.  The formal name for the square root sign (√) is the radical sign.

When a radical sign appears in an equation (as it often does in statistics), it has the same effect as parentheses on the order of operations.



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Last Modified:  06/28/2018

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