Expert: Bobby Soltani - 2/7/2005

Question
hi my math teacher is horrible im a senior and i have to take algebra 1 again i was wondering if there was an easier way to explain the following - zero and negative expontes. dividing exponetns. and scientific notation

thank you soo much
gaby  

Answer
Hi Gaby,

I'm not sure what part of those you are having trouble with.  However, here are some tips for each.

zero exponents - anything to the zero power is 1

1^0 = 1
35^0= 1
x^1 = 1

negative exponents - negative exponents are the same as saying one over the number.  For example, 3^-5 is the same as 1/(3^5).  Another example 2^-2 is the same as 1/(2^2) = 1/4.

Dividing exponents - to divide numbers with exponents, you just subtract the exponents.  Here's and example:

(5^6)/(5^4) = 5^2 = 25

6 - 4 = 2, so the final exponent is 2.  Notice that the base (in this case 5) must be the same.  Here's another example:

4^3/(4^-2)
3-(-2) = 5, so the answer is 4^5.

Scientific notation:  This is just a way of representing numbers.  For instance, the number 1000 could be written as 1*1000, or 10*100.  In scientific notation, we move the decimal point so that the number is between 1.0 and 9.99, then we multiply it by a 10 to the power of something so that the value is the same.  Here is an example:

500.0

We want the number between 1 and 9.99 so we will move the decimal point two spots to the left and get 5.  Moving the decimal point each time to the left is the same as dividing by 10 so we have to multiply the result by 10 each time so that the number doesn't change.  Here are the steps

=500
=50 x 10
=5 x 10 x 10
=5 x 10^2

If you have to move the decimal to the right, then the exponents are negative( since you are multiplying by 1/10 which equals 10^-1).

example:

0.043
=0.43 x 10^-1
=4.3 x 10^-1 x 10^-1
=4.3 x 10^-2

I hope this helps you.  Read the above information carefully.  If you have any other questions, let me know.

Bobby