course Mth 163 assignment #013013.
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18:14:40 `questionNumber 130000 `q001. Note that this assignment has 12 questions What does 2^5 mean?
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RESPONSE --> This stands for 2 to the 5th power or 2*2*2*2*2. confidence assessment: 3
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18:14:53 `questionNumber 130000 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.
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RESPONSE --> i see self critique assessment: 2
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18:15:57 `questionNumber 130000 `q002. What does 2^3 * 2^5 mean? Is the result of power of 2? If so, what power of 2 is it?
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RESPONSE --> It means (2*2*2)*(2*2*2*2*2) or 2^8 confidence assessment: 3
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18:16:07 `questionNumber 130000 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.
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RESPONSE --> i got it self critique assessment: 3
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18:16:50 `questionNumber 130000 `q003. Why do we say that a^b * a^c = a^(b+c)?
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RESPONSE --> b/c a must be to the power of b and c so it still means the same thing. confidence assessment: 2
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18:16:57 `questionNumber 130000 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).
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RESPONSE --> i see self critique assessment: 2
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18:19:22 `questionNumber 130000 `q004. What does (2^3)^5 mean?
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RESPONSE --> All you do is (2^3) five times, so you have (2^3)* (2^3)*(2^3)*(2^3)*(2^3) confidence assessment: 2
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18:19:31 `questionNumber 130000 Since 2^3 stands for 2*2*2, it follows that (2^3)^5 means (2^3)*(2^3)*(2^3)*(2^3)*(2^3) = (2*2*2)*(2*2*2)*(2*2*2)*(2*2*2)*(2*2*2) = 2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 = 2^15.
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RESPONSE --> ok self critique assessment: 2
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18:20:13 `questionNumber 130000 `q005. Why do we say that (a^b)^c = a^(b*c)?
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RESPONSE --> You just have to multiply the exponents to get the power. confidence assessment: 2
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18:20:22 `questionNumber 130000 We saw in the last example how (2^3)^5 stands for the product of 5 quantities, each equal to the product of three 2's. We saw how this is equivalent to the product of fifteen 2's, and we saw how the fifteen was obtained by multiplying the exponents 3 and 5. In the present question a^b stands for the quantity a multiplied by itself b times. (a^b)^c stands for the quantity a^b multiplied by itself c times, which is equivalent to multiplying a by itself b * c times. Thus we say that (a^b)^c = a^(b * c).
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RESPONSE --> i get it self critique assessment: 2
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18:21:44 `questionNumber 130000 `q006. According to the law a^b * a^c = a*(b+c), if we multiply 2^5 by 2^-2 what power of 2 should we get?
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RESPONSE --> the power of 2 that we get is =2^(5+-2)=2^3 confidence assessment: 2
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18:22:00 `questionNumber 130000 To according to the law, 2^5 * 2^-2 = 2^(5 + -2) = 2^(5-2) = 2^3.
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RESPONSE --> I understand when using the notes. self critique assessment: 2
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18:24:19 `questionNumber 130000 `q007. Since as we saw in the preceding question 2^5 * 2^-2 = 2^3, what therefore must be the value of 2^-2?
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RESPONSE --> I first found that 2^5 is 32 then 2^3 is 8. So I take 8/32 and get .25 for the value of 2^-2 confidence assessment: 2
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18:24:46 `questionNumber 130000 One way of seeing this is to note that 2^5 = 32 and 2^3 = 8, so we have 32 * 2^-2 = 8. Dividing both sides by 32 we get 2^-2 = 8 / 32 = 1/4. We can learn something important if we keep the calculation in powers of 2. If 2^5 * 2^-2 = 2^3, then dividing both sides of the equation by 2^5 we obtain 2^-2 = 2^3/2^5, which is equal to 1/2^2. This shows us that 2^-2 = 1/2^2.
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RESPONSE --> I got it. self critique assessment: 2
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12:07:06 `questionNumber 130000 `q008. Why must we say that 2^-n = 1 / 2^n, where n stands for any counting number?
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RESPONSE --> B/c 2^-n and 1/2n are equal confidence assessment: 3
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12:07:15 `questionNumber 130000 This is because for any number m, we have 2^m * 2^-n = 2^( m + -n) = 2^(m-n), and we also have 2^m * (1 / 2^n) = 2^m / 2^n = 2^(m-n). So whether we multiply 2^m by 2^-n or by 1 / 2^n we get the same result. This shows that 2^-n and 1 / 2^n are the same.
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RESPONSE --> ok self critique assessment: 3
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12:08:30 `questionNumber 130000 `q009. According to the law a^b * a^c = a*(b+c), if we multiply 2^3 by 2^-3 what power of 2 should we get? Since 2^-3 = 1 / 2^3, what number must we get when we multiply 2^3 by 2^-3?
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RESPONSE --> We would get 2^3*2^-3=2^3*1/2^3=1 confidence assessment: 2
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12:08:40 `questionNumber 130000 2^3 * 2^-3 = 2^(3 + -3) = 2^(3-3) = 2^0. Since 2^-3 = 1 / 2^3 it follows that 2^3 * 2^-3 = 2^3 * ( 1 / 2^3) = 1.
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RESPONSE --> i see self critique assessment: 3
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12:09:23 `questionNumber 130000 `q010. Continuing the last question, what therefore should be the value of 2^0?
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RESPONSE --> It would be 1. confidence assessment: 2
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12:09:32 `questionNumber 130000 Since 2^3 * 2^-3 = 2^0 and also 2^3 * 2^-3 = 1 we see that 2^0 must be 1.
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RESPONSE --> i got it self critique assessment: 3
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12:10:36 `questionNumber 130000 `q011. How do we solve the equation x^3 = 12?
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RESPONSE --> apply 1/3 rd power to each one then solve to find x=2.284 confidence assessment: 2
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12:10:59 `questionNumber 130000 We solve the equation by taking the 1/3 power of both sides: (x^3)^(1/3) = 12^(1/3), then by the law (a^b)^c = a^(bc) we have x^(3 * 1/3) = 12^(1/3), so that x^1 = 12^(1/3) or just x = 12^(1/3), which we can easily enough evaluate with a calculator. We obtain a result of approximately x = 2.29 .
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RESPONSE --> The answer was rounded up but we got very close to the same solution. self critique assessment: 2
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12:11:35 `questionNumber 130000 `q012. How do we solve the equation x^(5/2) = 44?
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RESPONSE --> Do the same as last taking 2/5 th power of each side to get x=4.536 confidence assessment: 2
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12:11:57 `questionNumber 130000 If we take the 2/5 power of both sides we get (x^(5/2))^(2/5) = 44^(2/5) or x^(5/2 * 2/5) = 44^(2/5) or x^1 = 44^(2/5) so that x = 44^(2/5). Evaluating by calculator you should obtain approximately x = 4.54.
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RESPONSE --> Again, the answer was rounded up but we got similar answers. self critique assessment: 2
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12:12:03 `questionNumber 130000 end program
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RESPONSE --> self critique assessment: 3
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