Exponents

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 A^N 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:

Also, keep in mind:  a^-m = 1/a^m
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 4^2×4, 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 (a^3×3) =a x a⁹ = a¹⁰
Now the equation becomes a¹⁰/a² = a⁸
Thus, the correct answer is option C.