Indices
If a number a is multiplied with itself n times (i.e., in continuous products a Ã— a Ã— a ... n times), where n is a positive integer, then it is called n^{th }power of a and it is denoted as a^{n}, where n is said to be the exponent or index of a and a is called the base.Laws of Indices
 ^{}
ExampleCalculate 2^{2 }Ã— 2^{3}.Solution2^{2 }Ã— 2^{3} = 2^{2+3 }= 2^{5} = 32
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ExampleCalculate (3^{2})^{3 }Ã— 3.Solution(3^{2})^{3 }Ã— 3 = 3^{(2x3) }Ã— 3 = 3^{6 }Ã— 3 = 2187

ExampleFind the value ofSolution

ExampleFind the value ofSolution

ExampleCalculate (4 Ã— 3 Ã— 2)^{2}.Solution(4 Ã— 3 Ã— 2)^{2} = 4^{2 }Ã— 3^{2 }Ã— 2^{2} = 16 Ã— 9 Ã— 4 = 576

ExampleCalculateSolution

ExampleCalculateSolution
 a^{0} = 1, where a â‰ 0
Note: Anything raised to the power zero is equal to unity.
Example: 4^{0} = 1
Some variations in the above rule:
4^{0} = 1 [Here, it is  (4^{0})]
(4)^{0 }= 1
 If a^{m }= a^{n}, then m = n
 If a^{m }= b^{m}, then a = b
Example
Find the value of x, if
Solution
Given:
Let us try and reduce the expression to the simplest possible form.
Let us try and reduce the expression to the simplest possible form.
Example
Simplify:
Solution
Try to reduce the expression to a simple form by combining terms with the same base.
Example
Find the value of
Solution
Writing the above expression in a form where the bases are same, we get,
Example
Simplify
Solution
.
Example
Simplify
Solution
We should try to combine terms with same base and cancel out any common factors.
Example
If then n = ?
Solution
Given: