2.7+Exponents+and+Roots

Section 2.7 - Exponents and Roots
We already learned about exponents and square roots, but when the minus sign gets involved it gets just a bit trickier, so here are some important things to understand about exponents and roots with negative numbers.


 * Negative Numbers as Bases**


 * The exponent only affects the thing (number or variable) right in front of it! **



In the second problem, the parentheses mean that the whole base is - 3, meaning that you would multiply - 3 by itself. Negative times a negative means a positive answer. However, in the last problem, the exponent is only affecting the three and not the minus sign. Because you do exponents before multiplication or subtraction in the order of operations, you multiply the base of 3 by itself, a positive answer, and then apply the negative sign, giving you a negative answer after all.


 * Negative Numbers as Exponents**

It is possible to have a negative number as the exponent, but it doesn't mean the same thing and you should not think about it until you get to it in a later chapter.


 * Square Roots with Negative Numbers**

The square root of 36 is 6, because 6 x 6 = 36. However, doesn't ( - 6 ) x ( - 6 ) also equal 36? So the square root of 36 could really be either 6 or - 6. We call these the positive and negative square roots. For this course, you can simply ignore the negative square root.

Trick question warning! What is the square root of - 36? What number, times itself, equals - 36? No number would fit here, so let's call it undefined. You will find a different way to do that problem in a later course, but for now, it just isn't possible.


 * Revisiting Order of Operations with all of the new stuff**

The same rules that applied to Order of Operations before (PEMDAS), apply with negative numbers, so be sure to try out the practice problems in this section!


 * Practice Problems for this Section**

**Where to from here?**
2.1 Integers 2.2 Absolute Value 2.3 Adding Integers 2.4 Subtracting Integers 2.5 Multiplying Integers 2.6 Dividing Integers 2.7 Exponents and Roots Chapter Two Summary Chapter Two Homework