Rules Of Exponents
After the basic understanding of the exponents, the next step is to understand the different rules of the exponents. To do the exponents properly in math there are the following rules of exponents need to be understood by the students in grade seven or higher.
1. Zero Exponent: Yes, there is zero exponent in math, which means a number can have zero power. The beauty of zero exponent rule, or you can say the trick about zero exponent is that its value is always equal to one. For example; consider the problem, 3º which is read as three to the power zero. The solution to this is “One”. Mathematically,
3º = 1
1º = 1
2º = 1
2005º = 1 or it can be written as (2005)º = 1
Or (3ab)º = 1
Care should be taken while working with negative sign with the base. A negative sign with the base does make a difference in the answer as explained below;
(-9)º = 1
But – 9º = – 1
2. Exponent Multiplication: When two exponents are multiplied their bases should be considered before starting to solve them. If two or more exponents getting multiplied with same base, powers are added to get a new exponent with the single base. For example;
2² x 2 = 2² x 2¹ = 2³
Therefore, when there are two or more exponential functions with the same base getting multiplied, collect their powers by adding them and write the new exponent using the single common base.
3. Dividing the exponents: When dividing two exponents with the same base their powers are subtracted to get the new exponent with a single base as shown below:
3³/3² = 3¹ = 3
Hence, when there are exponential functions getting divided having the same base, their powers can be collected by subtracting the power of the exponents in the denominator from the powers of the exponents in the numerator. This way the complex exponential problems can be simplified to an exponent with the single base.
4. Exponent of an exponent: There are many problems involving power of another power. To solve these kind of problems, both the powers are multiplied to get a new power as shown below in an example:
(2³)² = 2³Ë™² = 2^6 (which is 2 to the power 6)
Above are all the basic exponent rules, as per my little knowledge. I hope this representation on rules of exponents will help grade seven or higher grade students to become more confident in exponents and hence in math.