Exponents
Exponents are a method used to express products of the same number.
How would you write: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2?
Hard to repeat the above number in calculations, isn’t it?
Well, exponents provide us the solution to the above problem. The above number simply becomes: 29
The expression AN is called a power and it stands for A x A x A x A ……. x A , where there are N factors of A. A is called the base, and N is called the exponent. By definition, A0= 1
In order to solve any question involving exponents you must remember the 5 basic rules of exponents. These 5 rules are universally applicable and help you solve any exponent problem with ease. These rules are:

rules for exponents-1

Also, keep in mind:  a-m = 1/am
Let’s use some of the rules above and try to solve some problems using the tips given above.
Example 1: Which out of the following is equal to the expression 164 x 43?

  1. 222
  2. 220
  3. 48
  4. 412
  5. 410

Solution:
Let us reduce the expression to a common base. You should notice is that the number 16 can be expressed as 42. Thus, 164 x 43  becomes ( 42)4
( 42)4 is equal to 42×4, that is 48.
Thus, the original product becomes 48 x 43= 48+3 = 411= (22)11 = 222
Thus, the correct answer is option A.
Example 2: If a not equal to zero, a(a3)3/a2 is equal to:

  1. a6
  2. a7
  3. a8
  4. a9
  5. a10

Solution:
Let us first simplify the numerator.
a(a3)3= a (a3×3) =a x a9 = a10
Now the equation becomes a10/a2 = a8
Thus, the correct answer is option C.


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