Solving Positive and Negative Exponents

The exponent of a number tells how many times the number is to be multiplied by itself. Exponent is more commonly called as power or index.

In general,

     where,                                                                           

–           A is base

–          n is exponent (or power, or index)

In word Aⁿ could be called as A to the power b.

 Example 1:  6² = 6 × 6 = 36

 6² could be called as ‘6 to the power 3’, ‘6 to the second power’ or ‘6 squared’.

 Example 2: 2³ = 2 × 2 × 2 = 8

 2³ could be called as ‘2 to the power of 3, ‘2 to the third power’ or ‘2 cubed’

Example 3: 5⁴ = 5 × 5 × 5 × 5

5⁴ could be called as ‘5 to the power of 4’, ‘5 to the fourth power’ or ‘ 5 to the 4th’

 

Negative Exponent

 The negative exponent is opposite of positive exponent. It can be solved in either of the two ways:

 Method  1:  First calculate Aⁿ and then take the reciprocal.

 For example, 5^-3

 5 × 5 × 5 = 125

 So, 5^-3  = 1/125

 Method 2: First take the reciprocal and then calculate Aⁿ.

For example, 7^-2

7^-2 = 1 ÷ 7^-2 = 1/7²

       = 1/(7 × 7) = 1/49

Special case: Any number to the power of zero is 1.

i.e  A⁰ = 1