**Notes on Exponents and Place Value**

An exponent is used to tell how many times a number, called the base is used as a factor: It is written and a small, raised number to the right of its base:

For 5^{4} 5 is
the **base** and ^{4} is the **exponent**. This means
multiply the 5 by itself, four times.

5 X 5 X 5 X 5 5 is used as a factor four times.

Sometimes we refer to **
exponentiation** as raising a number to a **power**. For example
3^{4} can be read as three to the fourth power.

Any number raised to the
2nd power is said to be **squared** and any number raised to the third
power is said to be **cubed**.

Standard form is 625

Expanded form is 5 X 5 X 5 X 5 The easiest way of doing this is to multiply every pair:

25 X 25 = 625

**Power of Ten: ** Any
number that is an exponential form of 10. For example 100 is 10^{2},
10,000 is 10^{4}, 10 is 10^{1}.

How do we write the e**xpanded
form of numbers using exponents** for its power of ten: We sum up the
value of each digit by multiplying by its power of ten in exponential form.

We write the number 148,582 using different formats:

Standard form: 148,582

Expanded form: (1 X 100,000) + (4 X 10,000) + (8 X 1,000) + (5 X 100) + (8 X 10) + (2 X 1)

Expanded form using
exponents: (1 X 10^{5}) + (4 X 10^{4}) + (8 X 10^{3}) +
(5 X 10^{2}) + (8 X 10^{1}) + (2 X 10^{0})

Any number raised to the **
power of 1 **always equals that **
number**:

example:
10^{1 }= 10 and 4^{1} = 4

Any number
**raised to the zero power** always equals **
one**:

example :
10^{0} = 1 and 4^{0} = 1