assignment 8

Good work. You did well on most of the 'extra questions' and on the text questions.

How helpful are the publisher's CDs that come with the text?

If anything is not clear let me know, and include as many specifics as possible.

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22:03:33 Extra question. What is the simplified form of sqrt( 4 ( x+4)^2 ) and how did you get this result?

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RESPONSE --> sqrt( 4 ( x+4)^2 ) = sqrt(4) * sqrt (x+4)^2 = 2 * x+4

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22:03:40 ** sqrt(a b) = sqrt(a) * sqrt(b) and sqrt(x^2) = | x | (e.g., sqrt( 5^2 ) = sqrt(25) = 5; sqrt( (-5)^2 ) = sqrt(25) = 5. In the former case x = 5 so the result is x but in the latter x = -5 and the result is | x | ). Using these ideas we get sqrt( 4 ( x+4)^2 ) = sqrt(4) * sqrt( (x+4)^2 ) = 2 * | x+4 | **

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RESPONSE --> ok

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22:08:15 Extra Question: What is the simplified form of (24)^(1/3) and how did you get this result?

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RESPONSE --> (24)^(1/3)= 8^1/3*3^1/3= 2^3/3*3^1/3= 2*3^1/3

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22:08:20 ** (24)^(1/3) = (8 * 3)^(1/3) = 8^(1/3) * 3^(1/3) = 2 * 3^(1/3) **

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RESPONSE --> ok

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22:19:47 Extra Question: What is the simplified form of (x^2 y)^(1/3) * (125 x^3)^(1/3) / ( 8 x^3 y^4)^(1/3) and how did you get this result?

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RESPONSE --> (x^2 y)^(1/3) * (125 x^3)^(1/3) / ( 8 x^3 y^4)^(1/3)=expand out and &take care of roots (x^2y)^1/3*5x/2xy*y^1/3= cxl out ( x^(2/3) )5 / (2 y)

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22:19:53 ** (x^2y)^(1/3) * (125x^3)^(1/3)/ ( 8 x^3y^4)^(1/3) (x^(2/3)y^(1/3)* (5x)/[ 8^(1/3) * xy(y^(1/3)] (x^(2/3)(5x) / ( 2 xy) 5( x^(5/3)) / ( 2 xy) 5x(x^(2/3)) / ( 2 xy) 5 ( x^(2/3) ) / (2 y) **

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RESPONSE --> ok

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22:23:20 Extra Question: What is the simplified form of 2 sqrt(12) - 3 sqrt(27) and how did you get this result?

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RESPONSE --> 2 sqrt(12) - 3 sqrt(27)= 2sqrt3*4 -3sqrt9*3= 2*2 sqret3- 3*3 sqrt 3= -5sqrt3

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22:23:28 ** 2* sqrt(12) - 3*sqrt(27) can be written as 2* sqrt (4*3) - 3 * sqrt (9*3) by factoring out the maximum possible perfect square in each square root. This simplifies to 2* sqrt (4) sqrt(3) - 3 * sqrt (9) sqrt(3) = 2*2 sqrt 3 - 3*3 * sqrt 3 = } 4*sqrt3 - 9 * sqrt3 = -5sqrt3. **

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RESPONSE --> ok

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22:31:53 Extra Question: What is the simplified form of (2 sqrt(6) + 3) ( 3 sqrt(6)) and how did you get this result?

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RESPONSE --> (2 sqrt(6) + 3) ( 3 sqrt(6))=distribute out 2*sqrt6 * 3sqrt6 + 3*3sqrt6 (2*3)(sqrt6*sqrt6) + 9 sqrt6=group together likes 6*6 + 9sqrt(6) = 36+9+sqrert 6

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22:31:59 ** (2*sqrt(6) +3)(3*sqrt(6)) expands by the Distributive Law to give (2*sqrt(6) * 3sqrt(6) + 3*3sqrt(6)), which we rewrite as (2*3)(sqrt6*sqrt6) + 9 sqrt(6) = (6*6) + 9sqrt(6) = 36 +9sqrt(6). **

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RESPONSE --> ok

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22:33:44 Query R.8.42. What do you get when you rationalize the denominator of 3 / sqrt(2) and what steps did you follow to get this result?

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RESPONSE --> 3/sqrt(2)=multiply by sqrt 2= 3 sqrt 2/2

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22:33:51 ** Starting with 3/sqrt(2) we multiply numerator and denominator by sqrt(2) to get (2*sqrt(2))/(sqrt(2)*sqrt(2)) = (3 sqrt(2) ) /2.

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RESPONSE --> ok

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22:40:02 Query R.8.46. What do you get when you rationalize the denominator of sqrt(3) / (sqrt(7) - sqrt(2) ) and what steps did you follow to get this result?

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RESPONSE --> sqrt(3) / sqrt(7) - sqrt(2) =multiply by sqrt7+sqrt 2= sqrt3 *sqrt7 + 2 /sqrt7^2 - 2^2 = 7 - 4 = 3= sqrt(3) (sqrt(7) + 2) / 3

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22:40:08 ** Starting with sqrt(3)/(sqrt(7)-sqrt2) multiply both numerator and denominator by sqrt(7) + 2 to get (sqrt(3)* (sqrt(7) + 2))/ (sqrt(7) - 2)(sqrt(7) + 2). Since (a-b)(a+b) = a^2 - b^2 the denominator is (sqrt(7)+2 ) ( sqrt(7) - 2 ) = sqrt(7)^2 - 2^2 = 7 - 4 = 3 so we have sqrt(3) (sqrt(7) + 2) / 3.

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RESPONSE --> ok

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22:46:04 Extra Question: What steps did you follow to simplify (-8)^(-5/3) and what is your result?

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RESPONSE --> (-8)^(-5/3)=(sqrt-2^3)^-5 -2^-5=-32=1/32

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22:49:35 ** (-8)^(-5/3) = [ (-8)^(1/3) ] ^-5. Since -8^(1/3) is -2 we get [-2]^-5 = 1 / (-2)^5 = -1/32. **

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RESPONSE --> [-2]^-5 = 1 / (-2)^5 = -1/32 i don't know how both negatives did not make a positive when inverted??

When you multiply or divide two negatives you get a positive.

There is no rule that says that when you take a negative power of a negative number the result is positive.

a^(-b) = 1 / (a ^ b), and if a is negative, a^b can be positive or negative, depending on whether b is positive or negative.

For example (-2)^3 = -8, while (-2)^4 = 16.

So

(-2)^-3 would be 1 / (-2)^3 = 1 / (-8) = -1/8, which is negative while (-2)^(-4) would be 1 / (-2)^4 = 1/16 = 1/16, which is positive.

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22:53:15 query R.8.64. What steps did you follow to simplify (8/27)^(-2/3) and what is your result?

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RESPONSE --> (8/27)^(-2/3)= put in sqrt form and pull out the cubes 2^-2/3^-2= invert to make a positive= =9/4

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22:53:21 ** Starting with (8/27)^(-2/3) we can write as (8^(-2/3)/27^(-2/3)). Writing with positive exponents this becomes (27^(2/3)/8^(2/3)) 27^(2/3) = [ 27^(1/3) ] ^2 = 3^2 = 9 and 8^(2/3) = [ 8^(1/3) ] ^2 = 2^2 = 4 so the result is (27^(2/3)/8^(2/3)) = 9/4. **

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RESPONSE --> ok

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22:58:42 Extra Question: What steps did you follow to simplify 6^(5/4) / 6^(1/4) and what is your result?

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RESPONSE --> 6^(5/4) / 6^(1/4) = cxl out 6^5/4 - 1/4 = 6^4/4/1= 6/1=6

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22:58:55 ** Use the laws of exponents (mostly x^a / x^b = x^(a-b) as follows: 6^(5/4) / 6^(1/4) = 6^(5/4 - 1/4) = 6^1 = 6. **

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RESPONSE --> ok

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23:01:22 Extra Question: What steps did you follow to simplify (x^3)^(1/6) and what is your result, assuming that x is positive and expressing your result with only positive exponents?

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RESPONSE --> (x^3)^(1/6)=law of expon 3*1/6=.5 or 1/2 x^1/2

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23:01:26 ** Express radicals as exponents and use the laws of exponents. (x^3)^(1/6) = x^(3 * 1/6) = x^(1/2). **

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RESPONSE --> ok

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23:12:20 Extra Question: What steps did you follow to simplify (x^(1/2) / y^2) ^ 4 * (y^(1/3) / x^(-2/3) ) ^ 3 and what is your result, assuming that x is positive and expressing your result with only positive exponents?

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RESPONSE --> (x^(1/2) / y^2) ^ 4 * (y^(1/3) / x^(-2/3) ) ^ 3 = x^(1/2 * 4) / y^(2* 4) * y^(1/3 * 3) / x^(-2/3 * 3)=cxl out exponents x^2 / y^8 * y / x^-2 = x^2 * x^-2 / y^7 = x^4 / y^7

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23:12:25 ** (x^(1/2) / y^2) ^ 4 * (y^(1/3) / x^(-2/3) ) ^ 3 = x^(1/2 * 4) / y^(2* 4) * y^(1/3 * 3) / x^(-2/3 * 3)= x^2 / y^8 * y / x^(-2) = x^2 * x^2 / y^7 = x^4 / y^7. **

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RESPONSE --> ok

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23:24:44 query R.8.96. Factor 8 x^(1/3) - 4 x^(-2/3), x <> 0.

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RESPONSE --> 8 x^(1/3) - 4 x^(-2/3)=2*x^1/3-4^-2/3*x^-2/3= 2*x^1/3- 4 x^(-2/3) pretty hard

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23:24:52 ** To factor 8x^(1/3)- 4x^(-2/3) we first need to write the expression without negative exponents. To accomplish this we multiply through by x^(2/3) / x^(2/3), obtaining (8 x^(1/3 + 2/3) - 4x^(-2/3 + 2/3) / x^(2/3) = (8 x - 4) / x^(2/3). We then factor 2 out of the numerator to obtain 4 ( 2x - 1) / x^(2/3). Other correct forms include: ( 4x^(1/3) ) ( 2 - ( 1/x) ) 8 x^(1/3) - 4 / x^(2/3). **

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RESPONSE --> ok

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23:30:23 Query Add comments on any surprises or insights you experienced as a result of this assignment.

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RESPONSE --> this reveiw chapter was really hard it took me about a week and a half and going through everything 3 times to complete this. the book is not very explanitory in the means of this. also it only has items up to index of 3 which on the 'extra questions' had all diff amts and i really had no idea of what to do

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