**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: 2^{9}

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, A^{0}= 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 16*^{4}x 4^{3}?- 2
^{22} - 2
^{20} - 4
^{8} - 4
^{12} - 4
^{10}

*Solution:*

Let us reduce the expression to a common base. You should notice is that the number 16 can be expressed as 4^{2}. Thus, 16^{4} x 4^{3 } becomes ( 4^{2})^{4}

( 4^{2})^{4} is equal to 4^{2×4}, that is 4^{8}.

Thus, the original product becomes 4^{8} x 4^{3}= 4^{8+3} = 4^{11}= (2^{2})^{11} = 2^{22}

Thus, the correct answer is option A.

*Example 2: If a not equal to zero, a(a ^{3})^{3}/a^{2} is equal to:*

- a
^{6} - a
^{7} - a
^{8} - a
^{9} - a
^{10}

*Solution:*

Let us first simplify the numerator.

a(a^{3})^{3}= a (a^{3×3}) =a x a^{9} = a^{10}

Now the equation becomes a^{10}/a^{2} = a^{8}

Thus, the correct answer is option C.