Exponents are frightening in appearance, but rather simple mathematical formulas if you can bring yourself to look at them in the same way one looks at the English language when partaking in the popular form of the text message. When you text LOL, you are really saying ‘laughing out loud’ in the shortest, simplest form available. Exponents are kind of a mathematical equivalent with respect to the fact you are given an opportunity to write out an otherwise long problem in a short simple form without affecting the solution.
Exponents function to constantly increase the value of a given number. If, for example, the given number is 2 and the exponent (the smaller printed number appearing on the upper right side of the given number) is 4, the equation is read as 2 to the 4th power. This is merely the “shorthand” version of asking the solution for 2 X 2 X 2 X 2. It is asking you to multiply the given number by itself as many times as the exponent tells you to. The solution to 2 to the 4th power is 16 because 2 X 2 is 4. 4 X 2 is 8 and 8 x 2 is 16.
When working with exponents remembering the phrase ‘to the power of,’ is the key to understanding the problem. In the case of the above example, the problem is read as 2 to the 4th power. It tells you to multiply 2 by itself four times. There are three terms used to otherwise express an exponential problem. You may be asked to solve a problem that is “cubed,” “squared,” or simply, “to the power of one.” For example, if the exponent reads 6 “squared” it is merely referring to the 2nd power. Instead of saying 6 to the 2nd power, you would say 6 squared which means multiplying 6 by itself 2 times. Thus, 6 squared equals 36, the solution to 6 X 6.
Cube is another word used in place of “to the power of.” Cube always refers to the 3rd power. The solution to the exponent 3 cubed is 27. 3 cubed is asking you to multiply 3 by itself 3 different times. 3 X 3 X 3. We know 3 X 3 = 9 and 9 X 3 = 27. Therefore, 3 cubed = 27. Pretty simple stuff, eh?
On occasion you may hear the term, “to the first power.”Any number to the first power is simply itself. So, if you see a problem where a given number is to the first power, such a 7 to “the first power,” do not raise the value of the number 7. Simply leave it alone. It remains 7. It is not telling you to multiply the number, in this case 7, by itself once. Doing so, would actually be “squaring” the number. For example 7 x 7 is 49, or 7 squared, (7 to the 2nd power). 7 to the 1st power is merely 7. This is the power of one and that is a rule of exponents.
Multiplying multiple exponents is a lot less complicated than it sounds. The most important point to remember is, multiply your numbers, while adding your exponents. For example: the simple multiplication problem 5 X 5 = 25. There are no exponents in said example. However if asked for the solution to 5 “squared” X 5 “cubed,” you know the problem is asking for 5 “to the 2nd power” X 5 “to the 3rd power”. Add the exponents “2” and “3” for a total of 5. Multiply 5 X 5 for a total of 25. The answer is 25 to the 5th “power,” or 25 X itself 5 times.
Remembering these simple rules can take the mystery out of exponents, making solving exponents no more complicated or difficult than text messaging. Just remember, it’s a quick and easy way to write out an otherwise long sentence, or in the case of exponents, a long mathematical problem.