- To define index and base of a number
- To discuss the different laws of indices
- To evaluate expressions using the laws of indices
- INDEX OF A NUMBER- The index of a number tells how many times to use the number in a multiplication. It is written as a small number to the right and above the base number. It is also known as exponent or power.
- BASE OF A NUMBER- It is the number that gets multiplied when using an index or exponent.
- THE THREE BASIC LAWS OF INDICES For any real number x, y, m, and n, the following rules uphold:
- Multiplication Law/ Product Rule
- Division Law/Quotient Rule
- Power Law/Power Rule
- Other Laws:
- Understanding the laws of indices plays an important role in manipulating and simplifying expressions involving indices.
- Laws of indices can also be used to evaluate expressions involving indices without the use of calculators.
BASE AND INDEX OF A NUMBER
It is vital to get familiarized with the base and index of a number. This will become the foundation of learning the laws of indices. In the given example, 3 is raised to 5. Meaning, the base will be multiplied to itself five times.
If we will evaluate the given, 3 x 3 x 3 x 3 x 3 = 243.
LAWS OF INDICES
- Multiplication Law/ Product Rule – When expressions with the same base (x) are multiplied, the indices (m and n) are added.
1) 2) 3)
- Division Law/ Quotient Rule – When expressions with the same base (x) are divided, the indices (m and n) are subtracted.
1) 2) 3)
- Power Law/ Power Rule – When an expression is raised to a certain index and is raised again to another index, the indices (m and n) are multiplied.
1) 2) 3)
Find the value of the following series.