course Mth 158 ????€?x???z?x??v}?assignment #009009. `query 9
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14:47:56 R.9.6. What steps did you follow to simplify (-8)^(-5/3) and what is your result?
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RESPONSE --> Since the exponent is negative I moved it to the bottom of the fraction. 1/ -8^5/3. -8^5 = -32,768 then I took the cube root and got -32. So my final solution is 1/ -32. confidence assessment: 2
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14:48:33 ** (-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 --> I did some things different, but still got the correct answer. self critique assessment: 3
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14:50:49 R.9.12. What steps did you follow to simplify (8/27)^(-2/3) and what is your result?
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RESPONSE --> First I took the cube root of 8/27 and got 2/3. Then I sqared 2/3 and got 4/9. Since the 2 was negative I flipped the fraction to get a final answer of 9/4. confidence assessment: 2
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14:51:20 ** 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 --> Again, I did the steps different but still found the correct answer. self critique assessment: 3
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14:53:08 R.9.24. What steps did you follow to simplify 6^(5/4) / 6^(1/4) and what is your result?
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RESPONSE --> In this problem, an exponent is being divided by an exponent, so you subtract them to get 6^4/4 which equals 6^1=6. confidence assessment: 2
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14:53:21 ** 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 --> I got it. self critique assessment: 3
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14:54:48 R.9.36. 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 --> Because this is an exponent being raised to an exponent, I multiplied them together to get x^3/6 which equals x^1/2 or the sqrt(x) confidence assessment: 2
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14:55:06 ** 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 --> I got that one. self critique assessment: 3
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15:06:49 R.9.48. 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) is in simpliest terms (y^2)^4 = y ^8 (y^1/3) is in simpliest terms (x^(-2/3))^3= x^-2. I am left with (x^1/2) / (y^8)*(y^1/3)/ x^-2. Then I moved did y^8 * y^1/3 = y^8/3. Then I moved x^-2 beside y^8/3. Then I have (x^1/2) / (y^8/3 x^2). Since I have an exponent divided by an exponent I subtract them and move the x to the bottom of the fraction, that gives me 1/ (x^3/2 y^8/3) confidence assessment: 1
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15:08:47 ** (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 --> I messed up because I didn't realize that (x^1/2 / y^2) was grouped together, I see that now though. I know that x^-2 must be moved to make it positive. I can see that my mistake happened in the first part of the problem. self critique assessment: 2
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15:10:44 R.9.72. Factor 8 x^(1/3) - 4 x^(-2/3), x <> 0.
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RESPONSE --> I don't understand the question, how can x be greater than 0 and less that 0 at the same time? confidence assessment: 0
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15:12:03 ** 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 --> The x<>0 must have just been a typo. I understand how to factor this problem by multiplying everything by x^2/3, and how you got the correct answer. self critique assessment: 2 <> means 'greater or less', which is the same as 'not equal to'. Go by the statement of the problem in your text.
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15:13:02 Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> I realized that exponents can be tricky, and sometimes it is hard for me to decide which law to use to solve a particular problem. confidence assessment: 3
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