Indexes)in mathematics, the power or exponent is raised to a number or variable. For example in number 244 is the index of 2. The plural form of index is indices. In algebra we encounter constants and variables. The constant is a value that cannot be changed. While a variable quantity can be assigned any number or we can say its value can be changed. In algebra we work with indices in the form of numbers. Let's learn the laws/rules of indices along with formulas and solved examples.
Definition index
A number or variable can have an index. Index of a variable (or a constant) is a value raised to the power of the variable. The indexes are also calledmade of exponents. It indicates how many times a certain number should be multiplied. It is represented in the form:
-inM= a × a × a ×……× a (m gange)
Here a is the base and m is the index.
The index says to multiply a given number (or base) by itself the number of times equal to the index being raised to it. It is a compressed method for writing large numbers and calculations.
Example:23= 2×2×2=8
In the example, 2 is the base and 3 is the index.
indexlove
There are some basic rules or laws for indices that you need to understand before getting involved with indices. These laws are used in performing algebraic operations on indices and in solving the algebraic expressions including those.
Rule 1:If a constant or variable has the index '0', the result is equal to one, regardless of the base value.
Example:50= 1, 120= 1, j0= 1
Rule 2:If the index is a negative value, it can be represented as the inverse of the positive index, raised to the same variable.
Example:5-1= ⅕, 8-3=1/83
Rule 3:To multiply two variables with the same base, we need to add their powers and raise them to that base.
Example: 52.53= 52+3= 55
Rule 4:To divide two variables with the same base, we need to subtract the denominator from the numerator and raise it to this base.
Example:104/102= 104-2= 102
Rule 5:When a variable with one or the other index is again incremented with another index, both indices are multiplied together to the same basis.
Example:(82)3= 82.3= 86
Rule 6:When two variables with different bases but same index are multiplied together, we need to multiply its base and increase the same index to multiplied variables.
Example: 32.52= (3 x 5)2= 152
Rule 7:When two variables with different bases but same indices are shared, we are required to share the bases and increment the same index to them.
Example:32/52= (⅗)2
Rule 8:An index in the form of a fraction can be represented as the square root.
Example:61/2= √6
Index math problems
Question.1: Gang x4j3z2in xy5z-1
Solution: x4j3z2in xy5z-1
= x4.x .y3.y5.z2.z-1
= x4+1.y3+5.z2-1
= x5.y8.z
Question 2: Solve one3B2/in2B4
Solution: a3B2/in2B4
= a3-2B2-4
= a1B-2
= a b-2
= a/b2
Question 3: Find the value of 272/3.
Solution: 272/3
=3√272
= 32
= 9
FAQs
Index laws are the rules for simplifying expressions involving powers of the same base number. = ( 3 √ 27)2 = (3)2 = 9. (2) Watch out for powers of negative numbers. For example, (−2)3 = −8 and (−2)4 = 16, so (−x)5 = −x5 and (−x)6 = x6.
What is index in math with example? ›
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.
What is an index example? ›
Broad market indices track large segments of the market or a major asset class. Some examples are the S&P 500, the S&P Global BMI (Broad Market Index), the S&P/ASX 200, the S&P/TSX Composite, or the S&P GSCI for the commodities market. Sector Indices.
What is index law 3 simple? ›
The third law: brackets
If a term with a power is itself raised to a power then the powers are multiplied together.
What do you mean by index? ›
a. : a number (such as a ratio) derived from a series of observations and used as an indicator or measure. specifically : index number. b. : the ratio of one dimension of a thing (such as an anatomical structure) to another dimension.
What is an example of a simple index? ›
A simple index number is the ratio of two values representing the same variable, measured in two different situations or in two different periods. For example, a simple index number of price will give the relative variation of the price between the current period and a reference period.
What is the simple example of index number? ›
Index numbers are values expressed as a percentage of a single base figure. For example, if annual production of a particular chemical rose by 35%, output in the second year was 135% of that in the first year. In index terms, output in the two years was 100 and 135 respectively. Index numbers have no units.
What is index set with example? ›
In mathematics, an index set is a set whose members label (or index) members of another set. For instance, if the elements of a set A may be indexed or labeled by means of the elements of a set J, then J is an index set.
What is the index law in math? ›
Indices are used to show numbers that have been multiplied by themselves. They can also be used to represent roots, such as the square root, and some fractions. The laws of indices enable expressions involving powers to be manipulated more efficiently than writing them out in full.
How to multiply indices? ›
To multiply together two identical values or variables (letters) that are presented in index form, add the powers. Example: b 5 × b 3 = b 5 + 3 = b 8 .
For example, if Index A had a base value of 100 in January of 2015 and that value increased to 150 as of January 2018, the index value increased by 50% over that 3-year period.
What is index number in real life examples? ›
Index numbers in measurement and index statistics are commonly used to measure things such as inflation, cost of goods sold (COGS), stocks, and other economic indicators. There are many different types of index numbers, but two famous examples are the Consumer Price Index (CPI) and Dow Jones Industrial Average (DJIA).
What is an index legal? ›
INDEX Definition & Legal Meaning
A book containing references, alphabetically arranged, to the contents of a series or collection of volumes; or an addition to a single volume or set of volumes con- taining such references to its contents.
What is an example of statistical index? ›
Index numbers and indexes
Example: If the population of a town increased from 20,000 in 1988 to 21,000 in 1991, the population in 1991 was 105% of the population in 1988. Therefore, on a 1988 = 100 base, the population index for the town was 105 in 1991.
