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The First Law of Indices

Indices are a helpful tool in mathematics for concisely representing the process of taking power or root of a number. As a result, it is critical to comprehend the notion and rules of indices to utilize them subsequently in crucial applications. We’ll start with the formal notation for writing a number with an index, then the laws that govern it. So, let's get started!

An index is the power or exponent increased to a number or variable in mathematics. In number 24, for example, 4 is the index of 2. Indexes are the plural version of the index. Constants and variables are used in algebra. A constant is just a quantity that cannot be altered. On the other hand, a variable amount can be assigned any number, or its value can be changed. In algebra, we deal with numerical indices. An index can be assigned to a number or a variable. A variable’s index is a value raised to the power of the parameter. Indexes are often referred to as exponents. It indicates how many times a particular number must be multiplied. It is written as follows: xm = x*x*x*x*x*x*………….(m times) In the above example, x is known as the base and m is known as the index. An exponential expression comprises two parts: the base, represented as b, and the exponent, denoted as n. The general form of an exponential expression is b n. For example, 4*4*4 may be expressed in exponential form as 43, where 4 is the base and 3 is the exponent. The base is the initial component of an exponential number. A base is essentially a number or variable that is continually multiplied. On the other hand, the exponent is the second element, which is located in the top right corner of the base. The exponent indicates how many times the base will be raised by itself.

Law of Indices

Index laws provide us with principles for simplifying computations or expressions that include powers of the same base. This indicates that the more significant number or letter must be the same as the smaller number or letter. Whenever the bases are dissimilar, one cannot utilize indices laws to assess computations. There are various indices laws (also known as indices rules), including multiplication, dividing, power of 0, bracket, fractional powers and negative. The First Law of Indices: Multiplication Let’s just take an example below:

The first rule says that if the exponents have the same bases and different powers and they are in multiplication the indices of the exponents get added.

So, the above example can be written as:

Rules to Multiply Exponents with different bases

When the bases of two numbers or variables differ, we can multiply the expressions by applying some simple exponent principles. We have two options here:

When the bases differ, the abilities remain the same.

Consider two expressions, an and bn, with a different base but the same power. The bases, in this case, are a and b, and the power is n. When multiplying exponents of distinct bases and powers, the bases are multiplied first. It may be expressed numerically as

Conclusion

This was all about the introduction of exponents and the law of indices. In this article, only the first law of indices is described, there are two more laws of indices that are also important to study. The second law of indices is the division law of indices and the third law is the law of brackets. I hope this article helps the person reading this to prepare well for the exams and score good marks.