On this page, you can find the rules for multiplying and dividing exponents with the same base, ie equal base. In addition to the rules, below is a solved example for both multiplying and dividing exponents with the same base. More solved examples can be seen in the video, which can also be found below in the text.
Multiplying exponents with the same base
When multiplying exponents with the same base, the following formula applies:
from which it can be seen that when multiplying exponents with the same base! So the base remains unchanged after the multiplication! The final exponent represents the sum of the two different exponents that were given before the multiplication.
Example number 1: To determine the product:
The basis remains 5, and the degree in the result is obtained as a sum of the exponents 7 and 2. The result of task number 1 is:
If when solving this type of problem, one (two or more) of the exponents is a negative number, then the rules for adding integers apply during the calculation. If the degree is a fraction, the rules for adding fractions apply.
Dividing exponents with the same base
When dividing exponents with the same base, the following formula applies:
from which it can be seen that when dividing exponents with the same base, the base remains unchanged after the division, while the final exponent represents the difference from the first and second (in the appropriate order) exponents that were given before the division.
Example number 2: To determine the quotient:
The base remains the same 5, and the degree in the result is obtained as the difference between exponents 7 and 2 (7-2). The result of task number 2 is:
When dividing exponents with the same base, if the exponents are integers, we follow the rules for operating with integers. If exponents are fractions, the rules for adding and subtracting fractions apply.
Video Examples
Finally, in the video below, you can watch solving several example problems for multiplying and dividing exponents with the same base!
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