Question

Explain the laws of Indices[exponents].
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Answer 1

Answer:

Exponents (or Index Numbers)

The number y then is said to be equal to the number a raised to the power x. a is known as the base (the number which is to be multiplied by itself successively) and x is known as the power or index to which a is raised, or simply the exponent of a. x can be any real number.

Step-by-step explanation:

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Answer 2

Answer:

Index (indices) in Maths is the power or exponent which is raised to a number or a variable.

For example, in number 24, 4 is the index of 2. The plural form of index is indices.

In algebra, we come across constants and variables. The constant is a value which cannot be changed.

Whereas a variable quantity can be assigned any number or we can say its value can be changed.

In algebra, we deal with indices in terms of numbers. Let us learn the laws/rules of the indices along with formulas and solved examples.

Index Definition

A number or a variable may have an index. Index of a variable (or a constant) is a value that is raised to the power of the variable.

am = a × a × a ×……× a (m times)

Laws of Indices

There are some fundamental rules or laws of indices which are necessary to understand before we start dealing with indices. 

Rule 1: 

If a constant or variable has index as ‘0’, then the result will be equal to one, regardless of any base value.

If a constant or variable has index as ‘0’, then the result will be equal to one, regardless of any base value.a0 = 1

Rule 2: 

If the index is a negative value, then it can be shown as the reciprocal of the positive index raised to the same variable.

a-p = 1/ap

Rule 3: 

To multiply two variables with the same base, we need to add its powers and raise them to that base.

ap.aq = ap+q

Rule 4: 

To divide two variables with the same base, we need to subtract the power of denominator from the power of numerator and raise it to that base.

ap/aq = ap-q

Rule 5: 

When a variable with some index is again raised with different index, then both the indices are multiplied together raised to the power of the same base.

Rule 6: 

ap.bp = (ab)p

Rule 7: 

When two variables with different bases, but same indices are divided, we are required to divide the bases and raise the same index to it.

When two variables with different bases, but same indices are divided, we are required to divide the bases and raise the same index to it.ap/bp = (a/b)p