Exponents


 * **An exponent is something that raises a number or a variable to a power. It is a process of repeated multiplication. For example, the expression [[image:http://www.algebralab.org/img/ae0ab6cd-9f15-4d70-9dfb-5ec1f2c90be2.gif width="17" height="20"]] means to multiply 2 times itself 3 times or [[image:http://www.algebralab.org/img/3e07c37a-956f-4f5a-aa7b-f6896bdb27ff.gif width="75" height="15"]]. In [[image:http://www.algebralab.org/img/3e9c803c-1231-450d-94fb-6e475657ecb2.gif width="17" height="20"]], the 2 is called the base and the 3 is called the exponent . Both the base and the exponent can be either a number or a variable.

Each of the following is an example of an exponential expression. ** ||
 * __Rules of Exponents__

Formula: ADDING:If the bases of the exponential expressions that are multiplied are the same, then you can combine them into one expression by adding the exponents. For Ex:

Formula: Subtracting:If the bases of the exponents expressions that are divided are the same then you could combine them into one expression by subtracting the exponents. For Ex:

Formula: Multiplying:If the base of the exponents expressions that are rasied to any power then you must multiply the exponents. For Ex:** = __Zero Power__ =

For Ex:** = __Negative Power__ =
 * Ohhh and another thing is that if a base is ever power to a 0 the answer is allways 1.

For Ex: **
 * Here is another thing you should look for.If you ever get an exponent that is a negitive you must make it to a positive.

= Scientific Notation = = =
 * Is a way of writing really really huge numbers,and for wrting really really small numbers.**

1.4 ×104 is a proper example of scientific notation because** > .9 ×104 is a NOT proper example because** > 3.34 ×10½ is a NOT proper example because** > 4.34 ×10-55 is a proper example because**
 * a ×10n where 1 ≤ a ≤ 10 and n is an integer. In other words the number that we'll call "a" is is multiplied by 10, raised to some exponent n. This number "a" must be no smaller than 1 and no larger than 10. To illustrate this definition examine the following:
 * **1.4, which is "a" in this example, is not smaller than 1 and not larger than 10 so it's ok.**
 * **10's exponent is the integer 4.
 * **.9 which is "a" in this example, is smaller than 1 which is not allowed in scientific notation
 * **10's exponent is not an integer.
 * **4.34, which is "a" in this example, is not smaller than 1 and not larger than 10**
 * **10's exponent is the integer -55. Integers can be negative**

|| [[image:http://www.physics.uoguelph.ca/tutorials/exp/exp1.gif]] || [[image:http://www.physics.uoguelph.ca/tutorials/exp/exp2.gif]] ||
', were both the same:**
 * When introducing the equations, we mentioned a case of wee beasties. There were 10% increases in the population. One population began with a population of 100, and after a year, there were 110. The other population had a population of 5000, and one year later, it grew to 5500. Note the ratios of final to initial populations, 'N/[[image:http://www.physics.uoguelph.ca/tutorials/exp/Nnot.gif align="center"]]
 * As you can see, for a one year interval, this ratio was 1.1.

Exponential Decay:** Recall the two [|equations] for exponential growth and decay: Suppose some environmental stress reduced a population of 1000 wee beasties to 800 in two days. How many will there be 7 days after the intial count of 1000 wee beasties? This problem must be done in two steps. First, we use the information about the first 2 days to find the decay constant, 'k'. Second, we use 'k' and the time t = 7 days, and the intial population to find the final population. For the first step, the logarithmic form of the equation is most useful. We know ' ' (the initial population was 1000), 'N' (the final population was 800), 't' (the time period was 2 days). Substituting into the second equation, we get So our decay constant is k = -0.112 day
 * [[image:http://www.physics.uoguelph.ca/tutorials/exp/exp1.gif]] || [[image:http://www.physics.uoguelph.ca/tutorials/exp/exp2.gif]] ||