Assignment 13

#$&*

course Mth 163

2-25-13 1:06

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm . Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution. 013. ********************************************* Question: `q001. Note that this assignment has 12 questions What does 2^5 mean? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 2*2*2*2*2 = 32 confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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Given Solution: 2^5 stands for 2 raised to the fifth power; i.e., 2^5 = 2*2*2*2*2. The result of this calculation is 2^5 = 32. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique rating:ok

********************************************* Question: `q002. What does 2^3 * 2^5 mean? Is the result of power of 2? If so, what power of 2 is it? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 2*2*2*2*2*2*2*2 2^8=256 confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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Given Solution: 2^3 * 2^5 means (2*2*2) * (2*2*2*2*2). This is the same as 2*2*2*2*2*2*2*2, or 2^8. When we multiply this number out, we obtain 256. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique rating:ok

********************************************* Question: `q003. Why do we say that a^b * a^c = a^(b+c)? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: When you multiply exponents you add the “b” and “c” together. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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Given Solution: We saw in the preceding example that 2^3 * 2^5 stood for a product of three 2's, multiply by a product of five 2's. We saw also that the result was identical to a product of eight 2's. This was one instance of the general rule that when we multiply to different powers of the same number, the result is that number raised to the sum of the two powers. One general way to state this rule is to let a stand for the number that is being raised to the different powers, and let b and c stand for those powers. Then we get the statement a^b * a^c = a^(b+c). &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique rating:ok

@& In your solution you quoted a rule as opposed to giving an explanation (the given solution didn't give a great explanation either).
An explanation might go something like this:
a^b represents a string of a's multiplied together. The length of that string is b.
a^c represents a string of a's multiplied together. The length of that string is c.
The result is a string of multiplied a's, of length b + c. This string can be represented by the expression a^(b + c). *@

Assignment 13

#$&*

course Mth 163

2-25-13 1:06

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm

Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

013.

*********************************************

Question: `q001. Note that this assignment has 12 questions

What does 2^5 mean?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

2*2*2*2*2 = 32

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

2^5 stands for 2 raised to the fifth power; i.e., 2^5 = 2*2*2*2*2.

The result of this calculation is 2^5 = 32.

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

------------------------------------------------

Self-critique rating:ok

*********************************************

Question: `q002. What does 2^3 * 2^5 mean? Is the result of power of 2? If so, what power of 2 is it?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

2*2*2*2*2*2*2*2 2^8=256

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

2^3 * 2^5 means (2*2*2) * (2*2*2*2*2). This is the same as 2*2*2*2*2*2*2*2, or 2^8.

When we multiply this number out, we obtain 256.

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

------------------------------------------------

Self-critique rating:ok

*********************************************

Question: `q003. Why do we say that a^b * a^c = a^(b+c)?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

When you multiply exponents you add the “b” and “c” together.

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

We saw in the preceding example that 2^3 * 2^5 stood for a product of three 2's, multiply by a product of five 2's. We saw also that the result was identical to a product of eight 2's. This was one instance of the general rule that when we multiply to different powers of the same number, the result is that number raised to the sum of the two powers.

One general way to state this rule is to let a stand for the number that is being raised to the different powers, and let b and c stand for those powers. Then we get the statement a^b * a^c = a^(b+c).

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

------------------------------------------------

Self-critique rating:ok

@&
In your solution you quoted a rule as opposed to giving an explanation (the given solution didn't give a great explanation either).

An explanation might go something like this:

a^b represents a string of a's multiplied together. The length of that string is b.

a^c represents a string of a's multiplied together. The length of that string is c.

The result is a string of multiplied a's, of length b + c. This string can be represented by the expression a^(b + c).
*@