Exponents are shorthand for repeated multiplication of the same thing by itself. For instance, the shorthand for multiplying three copies of the number 5 is shown on the right-hand side of the "equals" sign in (5)(5)(5) = 5

^{3}. The "exponent", being 3 in this example, stands for however many times the value is being multiplied. The thing that's being multiplied, being5 in this example, is called the "base".

This process of using exponents is called "raising to a power", where the exponent is the "power". The expression "5

^{3}" is pronounced as "five, raised to the third power" or "five to the third". There are two specially-named powers: "to the second power" is generally pronounced as "squared", and "to the third power" is generally pronounced as "cubed". So "5

^{3}" is commonly pronounced as "five cubed".

When we deal with numbers, we usually just simplify; we'd rather deal with "27" than with "3

^{3}". But with variables, we need the exponents, because we'd rather deal with "

*x*

^{6}" than with "

*xxxxxx*".

From Math is Fun:

# Exponents

The

**exponent**of a number says**how many times**to use the number in a multiplication.
In

so

**8**the "2" says to use 8 twice in a multiplication,^{2}so

**8**^{2}= 8 × 8 = 64
In words: 8

^{2}could be called "8 to the power 2" or "8 to the second power", or simply "8 squared"*Exponents are also called Powers or Indices.*

Some more examples:

###
Example: **5**^{3} = 5 × 5 × 5 = 125

^{3}= 5 × 5 × 5 = 125

- In words: 5
^{3}could be called "5 to the third power", "5 to the power 3" or simply "5 cubed"

###
Example: **2**^{4} = 2 × 2 × 2 × 2 = 16

^{4}= 2 × 2 × 2 × 2 = 16

- In words: 2
^{4}could be called "2 to the fourth power" or "2 to the power 4" or simply "2 to the 4th"

Exponents make it easier to write and use many multiplications

Example:

**9**is easier to write and read than^{6}**9 × 9 × 9 × 9 × 9 × 9**
You can multiply

**any**number by itself**as many times**as you want using exponents.
Tonight's homework is worksheet 2-4. Feel free to use a calculator!

-Miss K :)

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