R2

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21:50:01 query R.2.46 (was R.2.36) Evaluate for x = -2, and y = 3 the expression (2x - 3) / y and explan how you got your result.

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RESPONSE --> 2x-3 / y = (2)(-2)-3 / 3 = -4-3 / 3 = -7 / 3

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21:55:28 ** Starting with | | 4x |- | 5y | | we substitute x=3 and y=-2 to get | | 4*3 | - | 5*-2 | | = | | 12 | - | -10 | | = | 12-10 | = | 2 | = 2. **

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RESPONSE --> I made the mistake of adding I I 12 I - I -10 I = 22 I am unclear as to why it is 12 - 10 instead of 12 +10

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21:56:15 query R.2.64 (was R.2.54) Explain what values, if any, must not be present in the domain of the expression (-9x^2 - x + 1) / (x^3 + x)

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RESPONSE --> x = 0

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21:56:33 ** The denominator of this expression cannot be zero, since division by zero is undefined. Since x^3 + x factors into (x^2 + 1) ( x ) we see that x^3 + x = 0 only if x^2 + 1 = 0 or x = 0. Since x^2 cannot be negative x^2 + 1 cannot be 0, so x = 0 is indeed the only value for which x^3 + x = 0. **

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RESPONSE --> I got this one correct

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21:59:19 query R.2.73 (was R.4.6). What is (-4)^-2 and how did you use the laws of exponents to get your result?

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RESPONSE --> (-4)(-4)= 16

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22:00:41 **Since a^-b = 1 / (a^b), we have (-4)^-2 = 1 / (-4)^2 = 1 / 16. **

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RESPONSE --> I don't believe this answer is the one for problem # 73

I'm not sure about #73, but do you understand that (-4)^(-2) is 1/16?

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22:05:23 query Extra Problem. What is (3^-2 * 5^3) / (3^2 * 5) and how did you use the laws of exponents to get your result?

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RESPONSE --> (3^2 * 5^3) / (3^2 * 5) = ( (3*3)*(5*5*5)) / ((3*3)*5)= (9*125) / (9*5) = 1125 / 45 = 225 / 9 = 15 / 1= 15

225/9 is 25, not 15.

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22:06:14 ** (3^(-2)*5^3)/(3^2*5). Grouping factors with like bases we have 3^(-2)/3^2 * 5^3 / 5. Using the fact that a^b / a^c = a^(b-c) we get 3^(-2 -2) * 5^(3-1), which gives us 3^-4 * 5^2. Using a^(-b) = 1 / a^b we get (1/3^4) * 5^2. Simplifying we have (1/81) * 25 = 25/81. **

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RESPONSE --> Is this the answer for the 'extra problem'??

It is. You calculated (3^2 * 5^3) / (3^2 * 5), not (3^-2 * 5^3) / (3^2 * 5).

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Your work looks good overall, but see my notes and be sure you understand how to handle negative exponents. Let me know if you have questions.