There are different types of laws of exponents and every rule of the exponent has to be utilised to solve different kinds of mathematical problems that will include the repeated multiplication procedures. The laws of exponents will help in simplifying the multiplication as well as division operations to further make sure that problems are very easily solved.
The exponents are the best possible representation of the repeated multiplication of a number by itself for example 7×7×7 can be represented as seven cubes and a cube which means three will be the exponent over here and will be the clear-cut indicator that seven has been multiplied three times. Seven will be the base over here which is the actual number that is getting multiplied so, other exponent rules or powers will help in denoting the number of times a particular number can be multiplied. If the power is 2 then it means that number has been multiplied two times.
The exponents will always follow different kinds of rules that will help in simplifying the expressions and are referred to as laws of exponents or rules of exponents.
Following are some of the very basic rules of exponents:
● The product with the same bases:
In this particular case when the base will be the same and the equation is of the product then the powers have to be added to conclude. For example, the case is five raised to power 5×5 raised to power one so the answer will come out to be five days to power 5+1 which is five raised to power six.
● The equation with the same bases:
This is very much similar to the above-mentioned rule and in this particular case the base will be the same but the powers will be subtracted whenever the terms will be in division form.
● Power raised to power form:
According to this particular law if there is a base and power has a further raised to power then the answer will come out to be by multiplying both the powers and the base will remain the same. For example, a question is two raised to power three and further raised to power three so the answer will come out to be two raised to power 3×3 which is to raise to power nine.
● Product to a power:
As per this particular rule for two or more different bases if the power will be the same then the base has to be divided and simplified to find out the answer. For example, the question is 15 raised to power 3÷5 raised to power three. So, here the simplification of 15÷5 will be carried out first and the answer will come out to be three days to power three which is 27.
● Zero power:
According to this particular rule when the power of any integer will be zero the overall value will come out to be one. For example, two raised to power zero then the answer will be one.
● Negative exponent rule:
According to this particular leave, the exponent will be negative then the individuals can change it into positive by writing the same value in the dominator as well as numerator will hold the value one. So, this is a very vital concept that has to be mastered by the students because of its prevalence in two different kinds of questions and utilisation in the whole process.
● Fractional exponent rule:
The fractional exponent rule will be utilised if the exponent will be in the fractional form and suppose the fraction is 1÷2 then it will be considered as the square root of the base.
Hence, all the above-mentioned rules must be mastered by the students whenever they are interested to learn the exponents because exponent rules are very much important in terms of solving different kinds of questions. Also and enrolling the students on platforms like Cuemath is a very good idea so that they can master the concepts of exponent rules perfectly.