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Letp = F,9=T=TFor the following propositions, select True or False for its correct evaluationQ4 1 PointP V (9 ^ 7) TrueFalse042 1 Point47) ^ (P 7q) TrueFalseQ433 1 ...

Question

Letp = F,9=T=TFor the following propositions, select True or False for its correct evaluationQ4 1 PointP V (9 ^ 7) TrueFalse042 1 Point47) ^ (P 7q) TrueFalseQ433 1 Point0 9) ^-(q er) TrueFalse

Letp = F,9=T=T For the following propositions, select True or False for its correct evaluation Q4 1 Point P V (9 ^ 7) True False 042 1 Point 47) ^ (P 7q) True False Q433 1 Point 0 9) ^-(q er) True False



Answers

Decide whether each statement is true or false. If false, tell why.
$$\left[\begin{array}{rrr}{2} & {4} & {-1} \\ {3} & {7} & {5} \\ {0} & {0} & {0}\end{array}\right]=\left[\begin{array}{lll}{2} & {4} & {-1} \\ {3} & {7} & {5}\end{array}\right]$$

Being asked to determine if the given statement is true or false. So the statement reads why square times Y. To the fifth is equal to Y. To the suburb. Well in this case we have to think back to our properties of exponents. In this case we're taking two terms that have the same base and we're multiplying them together. Well this would be an example of our product tool. So let's review how the product rule works. It says that if we have a. To the empower and we multiply it by the same base. A raised to another power. The result is that same base. In this case a raise to the M plus M. Power. So in other words when you multiply to terms with the same bees, all you need to do is add their exponents. So let's apply this to our problem. So we have y squared times wide to the 5th. Both terms have the same base so our base will stay the same. And then we simply just add the exponents 2-plus 5. Well two plus five is equal to seven. So perfect. We've now found that Y squared times Y to the fifth is in fact quite to the seventh, which means our original statement was true.

Okay. We have to decide if this statement is true or false now, using the properties of exponents. I know that this is the same thing at Savage. The 1/2 plus 1/2 and we want to know. Does this equal 49? Well, this is just seven to the first power, and it does no equal 49. So I'm gonna backtrack a little bit and go. Well, I know that seven to the second power is equal to 49. She let me write that on the new line. Seven to the second power equals 49. How can I make this a second power? Maybe two, um, seven to be 1/2 times four to the fourth power. So that's when we can make this statement true. Try to think, or you could even do seven to the first time. Seven to the first equals 49. So these are a couple of different needs to break the true statement.

Though seven of the one halftime seven of the 1/2 that is seven to the 1/2 plus 1/2. Because when we're multiplying numbers the same base were supposed to add the exponents, which is seven to the first power, Um, which is just seven, not 49. So let's correct that incorrect statement. So first of all, we'll say false on and make the necessary changes. So how about we do seven to the 1/2 time? Seven to the 1/2 just equals seven. There's my change. I change the 49 to a seven.

In this problem, we are given that an equation, why do the barbecue is equal two X. to the Power P. Repeating here are integers. And we're required to find out whether the statement a few times Why I raised to the power P -1 is equal to be dimes X rays to the power p minus one is correct. Sorry, this was a Q. Over here, not a P. So we regard to find out if this is true or false. So let's start with our equation and take differential operator on both sides. So we're going to differentiate implicitly with the risk with regards to the variables. So the differential of why do the barbecue is simply Q. Times. Why did the power Q -1 time's D. Y. So the differential dy comes as well and we'll do the same for the right hand side. And we get p times x rays to the P -1 times dx. So we'll notice our original equation and it's missing a dy and dx. So this equation is false. So it's incorrect and are correct. Equation has the differentials Dy and DX and them as well.


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