# Properties of Exponents

An exponent is the power written at the top right hand side of a number (base value). Like many others, are you too boggled by the properties of exponents? This Buzzle article will give you a brief yet simple explanation of the same.

Shalu Bhatti

Meaning

^{5}, where 2 is the base value and 5 is the exponent value. The value of 2

^{5}= 2 x 2 x 2 x 2 x 2 = 32. Therefore an exponent, which is also known as an index or power, is the number which represents that how many times the base value needs to be multiplied with itself.

Properties

Multiplication

The multiplication property states that, if the same base value with different exponents are multiplied with each other, then the exponent value can be added together. To make this statement clear, let's take this example:

*5*Here, if we omit the parentheses, we will have the product of five 5s, which is written as 5^{2}x 5^{3}= (5 x 5) x (5 x 5 x 5) = 5^{5}.^{5}, which is the same as the added value of both the exponents 2 and 3. Therefore, the multiplication property of exponents is,*a*.^{2}x a^{3}= a^{2+3}= a^{5}Division

When you divide two different exponents having the same base, the exponents' values should be subtracted to get the correct answer. For example,

*5*. The answer will be same if you do the long method of dividing each and every base and exponent. Therefore, remember this property and save your time. Remember, this is valid only when the base value is the same.^{3}/ 5^{2}= 5^{3-2}= 5^{1}Power of Quotient

The power of a quotient property states that when a and b are base values wherein b is not equal to 0, and c is the exponent value provided both a and c are not 0, then, a

^{c}/b^{c}= (a/b)^{c}. In short, if the exponent value of both the numerator and the denominator is the same, and the values mentioned above are not zero, then the exponent value for the whole fraction becomes the same.Zero Exponents

It's true that anything multiplied by 0 is 0. But when it comes to exponential properties, anything raised to the power value 0 is '1'. Let's take an example,

*5*. Now, we know that 5^{0}x 5^{1}= 5^{(0+1)}= 5^{1}^{1}= 5, therefore, 5^{0}x 5 = 5, meaning the value of 5^{0}being 1. PS: The value of 0^{0}is undefined.Negative Exponents

This property comes into picture when dealing with negative exponents. It is explained with the help of this example:

*5*. You can have a look at the solved example that follows, which will make this property clearer to you. 5^{-2}= 1/5^{2}^{-2}x 5^{2}= 5^{(-2+2)}= 5^{0}, 5^{2}= 25, and 5^{0}= 1. Therefore, 5^{-2}= 1/25.