Precalc

Fall 2002

Handout #1

Everything You Ever Wanted to Know About Exponents

The number 3 is the exponent, also called the power. The x is called the base.

The exponent tells how many times the base is to be multiplied by itself.

Thatís why you can say and why, in general,

 

the formula is correct. Explain why that formula works. ______________________________________________________________________________________

 

 

______________________________________________________________________________________

Now, suppose you have This you can write as . That seems right. Now how about using that other way of simplifying: . This gives you . This shows that .

Explain why this makes sense to you or explain why you have a problem with it. __________________

 

 

______________________________________________________________________________________

Using this technique, you can show that and and in general, .

Rewrite as an expression that does not look like a fraction. ______________________________

Now, recall that . Similarly, . So, it is possible to rewrite as . So, the following statement is also true: .

Rewrite the following expressions so that they do not look like fractions.

 

 

 

Now, for something that seems completely different, but really isnít.

= 3 because (3)(3) = 9_____________________________________________

= because

because

because

because

because x * x = x

 

 

 

 

So, if I say simplify , you could write =

 

 

 

 

 

Now, simplify these expressions.

 

-() (-)

Ellen Bragar Knapp

 

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 last updated 12/19/2005 03:03 PM