Laws of Exponents
There are seven laws of exponents that we study under this heading.
Product of Power Rule: This rule states that two numbers in exponential having the same base are multiplied then their product contains the same base and their powers get added. For Example 23⨯24 = 23+4 = 27
Quotient of Power Rule: This rule states that two numbers in exponential form is divided then the quotient has the same base and their powers get subtracted. For Example: 35/32 = 35-2 = 33
Power of Power Rule: If a number in exponential form is raised to some power then its powers get multiplied. For Example, (43)2 = 43⨯2 = 46
Power of a Product Rule: If two numbers in the exponential form that have the different bases but the same exponents are multiplied then the product has the base equal to the product of two bases and the power remains the same. For Example, 32⨯42 = 122 = 144
Power of Quotient Rule: If two numbers in the exponential form that have a different base but the same exponents are divided then the quotient has the base equal to the quotient of two bases and the power remains the same. For Example, 63/33 = 23 = 8
Zero Exponent Rule: Any number raised to power zero gives 1. For Example, (101)0 = 1
Negative Exponent Rule: If any number is raised to negative power then to make the power positive, the base is converted to its reciprocal. For Example, 2-3 = (1/2)3 = 1/23 = 1/8
Exponents
Exponents are the basic concept used in mathematics that are helpful in solving and understanding very large numbers. Suppose we have to simplify a very large number such as 10 multiplied by itself 10 times then the number is represented as, 1010 which is a very easy way of representing the numbers. Exponent is also called the power of a number. The exponent of the number can be integers or fractions, The fraction exponent is also called the radical.
Table of Content
- What are Exponents?
- Exponents Formulas
- Laws of Exponents
- Exponents with Fractions
- Exponent Table