**
EXPONENTS**

** 5 ^{3 =}
(5)(5)(5) = 125 5^{3} 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.

**
4 ^{2} = (4)(4) = 16
4^{5} = 1024**

By definition any
number with a 0 exponent is = to 1.
So 4^{0}^{ } = 1,
9876545679309^{0} = 1

The one exception is 0^{0} which is not defined.

We can work in the
opposite direction. 25 can be changed to a base and exponent. 25 = 5^{2}

81 = 9^{2} or 3^{4}

7 x 7 x 7 x 7 x 7 x
7 can be written 7^{6}.

Exponents in algebra
mean the same as in arithmetic.

T^{3} means
T x T x T.

**
In
algebraic multiplication problems we
add exponents when the bases are the same.
Example A ^{2 } x
A^{4} = A ^{2 + 4 } = A^{6}**

**In
algebra when we divide terms with the same bases we subtract exponents. Example
t ^{5}/t^{3} = t^{5 – 3 =}
t^{2 }**

**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 3 ^{2} / 3^{2}
= 3^{2} ^{- 2} = 3^{0} and 3^{0 }must =1
because 3^{2} = 9 and 3^{2} / 3^{2} = 9/9 =1 (The above
rule from arithmetic that any number divided by itself must equal 1) a^{3}/a^{3
} = a^{3 – 3} = a^{0}
=1 by definition of zero exponent. If a^{0} 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.

**Therefore by definition any
number with a 0 exponent is = to 1.
So 4 ^{0}^{ } = 1,
9876545679309^{0} = 1 **

The one exception is 0^{0} which is not defined.

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