EXPONENTS

53  = (5)(5)(5) = 125   53  means to multiply 5  three times. The 5 is called
the base and the 3 is the exponent.
The meaning of exponents is the same at all levels of mathematics.
For example:  (x + 3)2 means to multiply (x + 3) times (x + 3).  This is why people say that
exponents are a short way of indicating multiplication.

42 = (4)(4) = 16
45 = 1024

By definition any number with a 0 exponent is  =  to 1.  So  40  = 1,  98765456793090 = 1
The one exception is 00 which is not defined.

We can work in the opposite direction. 25 can be changed to a base and exponent. 25 = 52
81 = 92 or 34

7 x 7 x 7 x 7 x 7 x 7 can be written 76.

Exponents in algebra mean the same as in arithmetic.

T3 means T x T x T.

In algebraic multiplication problems we add exponents when the bases are the same.     Example A2  x  A4 = A 2 + 4  = A6

In algebra when we divide terms with the same bases we subtract exponents. Example t5/t3 = t5 – 3  = t2

Think   3/3 = 1    a/a =1 any number divided by itself equals one. Therefore following the rule that we subtract exponents when we divide 32 / 32 = 32 - 2 = 30 and 30 must =1  because 32 = 9 and 32 / 32 = 9/9 =1 (The above rule from arithmetic that any number divided by itself must equal 1)  a3/a3  = a3 – 3 = a0 =1 by definition of zero exponent. If a0 did not equal one then our mathematical system would have a major flaw because any number divided by itself would not equal 1 and the rule of subtracting exponents when we divide would not work.  Think;  34/34 = 81/81 which = 1  therefore 34/34 = 3 4 - 4 = 30 which must = 1 or else we have a major contradiction in our mathematical system.

Therefore by definition any number with a 0 exponent is  =  to 1.  So  40  = 1,  98765456793090 = 1
The one exception is 00 which is not defined.
Why isn't 00  defined?