What are the main exponent rules?

Rules of Exponents: There are 4 basic exponent rules. Students in grade 7 and beyond need to be familiar with these rules and should be able to apply these rules when dealing with problems involving exponents.

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Zero Exponent Rule or Power Zero Rule: This is a very very basic rule to remember as most often overlooked by students and which cost them lot of marks in their math quizzes and exams. The rule is that "If any number raised to the power of zero then its value is equal to one". 

For example; consider the problem, 2º which is read as two raised to the power zero. The answer is equal to 1 as shown below:

2º = 1 

Below are more example on zero exponent law

5º = 1 

9º = 1 

Or in case of algebra      (5xy)º = 1 

Make sure you do it right when there involves negative number as the base. Look at the example below to understand how the negative sign can change the answer when parenthesis are used  and when not used:

 (-3)º = 1          but   -3º = - 1   

2. Law of Exponent Multiplication: In case there are two exponents being multiplied and their bases are the same then we can add the powers (exponents) to get the new power (exponent) and base remains the same. For example; 

5² x 5          {we can write it as follows as 5 can be written as 5¹}

= 5² x 5¹   { add the powers 2 and 1 to get the new power as 3 and base remains the same}

 = 5³     

3. Law of Exponent  Division: If we divide two exponential terms and their bases are same then we subtract the power of the denominator from the power of the numerator to get the new power and base remains the same. For example; 

3³/3² 

= 3¹     {But 3¹ is same as 3 hence we can write the final answer as shown below}

= 3   

4. Exponent of an exponent: There is another rule involving exponents which is exponent of another exponents. These problems look like (3³)²  and to solve it just multiply both the exponents to get the new exponent and base remains the same. We can solve it as follows 

(3³)² = 3³˙² = 3^6 (which is 3 raised to the power of 6) 

Below is a practice sheet to practice all the laws of exponents

Click for pdf format of above worksheet