Thursday, March 12- Exponents and Square Roots

Exponents

Exponents are used to denote the repeated multiplication of a number by itself. 
 

For example, 24 = 2 × 2 × 2 × 2 = 16
In the expression, 24, 2 is called the base, 4 is called the exponent, and we read the expression as “2 to the fourth power.”

When the exponent is 2, we call the process squaring. 
For example,
52 = 25, is read as "5 squared is 25".
62 = 36, is read as "6 squared is 36".
 

When negative numbers are raised to powers, the result may be positive or negative. A negative number raised to an even power is always positive, and a negative number raised to an odd power is always negative.

For example, 
(−3)4 = −3 × −3 × −3 × −3 = 81 
(−3)3= −3 × −3 × −3 = −27Take note of the parenthesis: (−3)2 = 9, but −32 = −9
 

Zero or Negative Exponents

Exponents can also be negative or zero; such exponents are defined as follows. 
• For all nonzero numbers a, a0 = 1. 
• The expression 00 is undefined.
 

Square Roots

A square root of a nonnegative number n is a number r such that r2 = n. 
For example, 5 is a square root of 25 because 52 = 25. 
Another square root of 25 is −5 because (−5)2 is also equals to 25.

The only square root of 0 is 0. Square roots of negative numbers are not defined in the real number system.

Perfect squares and square roots

Some numbers are called perfect squares. It is important we can recognize perfect square when working with square roots.
12 = 1
22 = 4
32 = 9 
42 = 16
52 = 25
62 = 36 
72 = 49 
82 = 64
92 = 81
102 = 100