Zero, Negative, and Fraction Exponents [CC] – Free Civil Service Review

Zero, Negative, and Fraction Exponents [CC] – Free Civil Service Review


Hi there, thank you for checking out my
channel. Thank you for clicking on this video. This video is part of a series of
videos I’m posting to try to help people out when it comes to aptitude tests like the Civil Service Exam. This video in particular is part of my series on Math.
Today, we’re going to talk about Exponents. But not just any exponents, because we already have discussion regarding that, if you haven’t seen the series on exponents yet, we talked about addition, subtraction, multiplication and division of exponents. You can click
right here. Today, we are going to talk about something different which is special cases of exponent, and that is actually found in the workbook, if
you have a copy of workbook number one, it’s on page 10 of the workbook. So
we’re going to answer SOLVE THESE WITH ME part, I’m going to show you how
to do it and in order for me to show you better, I’m going to switch over to my
PC. See you in a bit. We’re going to talk about exponents, special exponents, this means weird exponents that possibly be included in the exam. I’m teaching you this because when I took the exam it was included and I knew that if you’re not familiar with this, this would have been a really easy question to
answer, but you might get confuse and your time runs out or we really can’t answer it. Okay? I’m going to take this one question at a time, for those who have workbook make sure that you focus and if you don’t understand at
the beginning, make sure that you repeat it until you understand it. That’s the reason I make videos, okay? SOLVE THESE WITH ME number one, 54321 raised to zero. Now, that zero, what you have to remember is that, any number if you raised it to zero, if the exponent is zero, even if it is x raise to zero, it’s always going to be 1. The answer will always be 1. It doesn’t matter whether a number is big or small,
anything raised to zero becomes 1, okay? That’s just something that you have to
remember. Next question, what if negative exponent and this is something
that one of the people who took the test last time asked because it appeared on his test booklet, actually, it also appeared on my test booklet. There’s something
that you have to remember and I want you to pay close attention, that is for Team Lyqa, okay? Because if it is nega (negative), it will fall down. That’s what you need to remember. Why? Because if the exponent is negative, the whole numbers will fall. Let me show you. That negative 1, 210 raised to negative 1, becomes 1 over, will fall down, 210 raised to 1 or 1 over 210, okay? Again, if it is nega, it will fall down, so any number that is negative will fall down and becomes fraction. For example, 1 over .. scratch that .. 2 raised to negative 2 that is going to be a fraction then it will fall down, so 1 over 2 squared, okay? That’s something to remember. Now, I’m
going to ask you to try to solve this next question using all the things that
you learned today in this snippet of the lesson, okay? So hit pause now, try to
answer that for now. All right. Let’s see how you did okay this is part of our
learning process make sure you follow along try to answer the questions so you’ll have your own practice, okay? Here, it looks a little complicated because a lot of things is happening and this kind of question usually appeared in the exam when it comes to special exponent but the key here is to know what they mean. This x raised to zero, don’t be scared, that becomes just 1, so it’s something that
you can ignore. And this y raised to negative 2, since it is negative 2, it will fall down what will happen is, this becomes the denominator, becomes y squared, okay? and then you have 1 times 1. This 1 here, and this 1 on the fraction of 1 over y squared. So again, nothing is happening in the numerator, okay? It becomes 1, because 1 times 1 is still 1. Okay? Now you’re done in the numerator, let’s go to denominator. Here, you have xy raised to zero. Now, a lot of people gets confuse to what they should simplify first, should they multiply xy to zero? Is it going to be 1 or is it going to be x? Okay? Always remember our PEMDAS. We already talked about this, so if you haven’t watch that video, go ahead
and watch that first. Simplify exponent before multiplication. x and y is multiplication, this is exponent, so this should be simplified first, y raised to zero, this becomes 1. So meaning, becomes x times 1 or just x. That’s what will also remain in the denominator, so x. So the answer becomes 1 over xy squared. It looks complicated, right? But if you know the technique, it’s really easy. So that is what I
want you to learn today, okay? Again, if you have to repeat it, practice, go ahead. Next, you have these, these equations that I already talked
about this in an earlier video but I just want to solidify the concepts, okay? So you have multiplication, in multiplications if they have the same First Name, I called this First Name, okay? And this is the Last Name or Surname. If they have the same First Name, both are 5, you can just copy the First Name. So you have 5 and
then the Last Name, you have to combine them. You’re going to add it, 2 plus
9 which is going to give you 11. So the answer is 5 raised to 11. The concept here is if for example, you will introduce Juan Cruz and Juan Santos, to save time, we’ll say, this is Juan Cruz and Santos. So we copied Juan since they have the same, and then add their Last Name, 5 raised to 11. In division, it is the opposite. Okay? It is still going to be Juan, or that’s the First Name so we have 8, but since it is the opposite of multiplication, and when you multiply, you add them. What is the opposite of addition? Subtraction. So this becomes 7 minus 3. So that is 4. So 8 raised to 4. Again, there’s a video about this. I discussed this more at length you can go and watch
those but we’re going to use that to solve this question. In order for you to try this out for yourself. Hit pause now. All right, let’s see how you did. Okay. What we will do is just to multiply this terms in the numerator. You have x cubed times x squared. Since they have the same First Name, just copy x and then add, 3 plus 2 is 5. x raised to 5.
Same thing here, you have x, they are both x. This is raised to 2. If it has no exponent, automatic, it is 1. So 2 plus 1 is 3. So x to the fifth over x cubed. So since this is division, we will subtract them, same First Name, x, then they
have 5 minus 3 which is going to be 2. So the answer here is x squared, okay? So practice and practice so you’ll get faster. Next, how about these? How about if they have exponent? This is the trick, all right, if you see like this, a number has exponent, parenthesis and then another exponent, okay, what you have to
understand is when you are using an exponent, for example, x squared. How do we simplify this? We repeat x based on the value here. So that’s x times x. If this is x cubed, add another x. What does this mean? 4 cubed raised to 5 is like you write five 4 cubed, okay? Meaning, you have to repeat it five times. So if we multiply them, like what we always say, if they have the same First Name, it should be remained, so 4. Then combine their Last Name. So you have 3, 6, 9, 12, 15. Now, is there a faster way to do that? If you look here, in this question, you can multiply, 3 times 5. In exponent, multiply. So 3 times
5. Now, for the next number. Why do I emphasized this? A lot of people made mistake here. What should be done here is, to remember your PEMDAS, okay? Parentheses, Exponents,
Multiplication, Division, Addition, Subtraction. Let’s go to parenthesis first. 5 times 2, this is going to be 10 and this is what we will cubed. That is going to be 10 times 10 times
10. Okay? So that is 10, times 10 which is
going to give you another zero, times 10, that is going to be 1000, okay? So let’s
try this on our sample question, okay? So hit pause now. All right, let’s see how you did, if you got it right. In the numerator you have 3 raised to 2 then raised to 3, so what we will do is 3, 2 times 3 which is 6. In the denominator, you have 3 times 2 which is actually 6 then you have squared, okay? So 6 squared. Now, do I need to multiply 3 raised to 6 times then divide it to 36 in case the options are entire numbers? I’m going to show you
another trick that I do, this is related to factoring. So 3 times 6 over and then you have 6 times 6 basically, right? 6 times
6 can be, 6 times 6 or 3 times 2, times 3 times 2. Now, if you notice
here, you have six 3s. Can I cancel a number? Is there a 3 in the denominator? Because the concept would be this, if 3 3 3
for example, over 3 3, 3 times 3 times 3 times 3 divided by 3 times 3. I can cancel this, provided, it has the same number in the denominator, right? So that is what we are going to do
here, you have one, two, you have two 3s in the denominator. Meaning, that two, we will subtract if from 6. That is going to be 3 raised to 4 over, what was remained was 2 and 2, which is 4. Here, it is easier to get the answer. So 3 times 3 is 9, times 3 is 27, 27 times 3, 21, then you have 81, 81 over 4. It is easier to manage instead of 3 times 3 times 3 times 3 times 3. At least, we reduce a few seconds when we’re solving, okay? Number 7, now this is the weirdest exponent yet and most people
don’t really know what to do with this that’s why if they saw this, they just skip or next number, they’ll just choose any letter. But I’m going to give you a clue on how to do it. I’m going to show you what you should do if the exponent is a fraction. So 4 raised to one-half or sometimes, it is written like this, okay. 4 raised to one-half. What we should do? If the exponent is a fraction, it’s actually a root. What does this mean? 4 raised to one-half is actually square root of 4. Why? Because, one-half square root. Another example, 8 raised to one-third, that is, following the pattern, cube root of 8. Meaning, 4 raised to one-half, is the square root of 4 which is 2, okay? So let’s
solve this using that information. I’m going to ask you to hit pause now. All right, let’s see how you did. In the numerator, you have one-half exponent of 400. So that is going to be square root
of 400 over and then you have here 125 and its exponent is one-third. So that is the cube root of 125. And now that we know that we can start solving. So 40, we use this in exponents, so if you haven’t seen
exponents lesson make sure that you watch that so you’ll understand what I am doing. So 400, okay, if we split this, it can be 20 times 20, okay? And since this is already two, these is what we need in exponent, so there are two 20s, you can cancel it. That is going to be 20. 20 is in the numerator. In the denominator, you have 125 but since this is cube root, you have to cancel three times. So 125 divided by 5, we can start with that, 5
you have 25, and this 25, it can be 5 and 5. So meaning, you have three 5, one, two, three. You can now put it outside the root. So that is going to
be over 5. The answer becomes 4. That’s simple. But the problem to us is that, sometimes, when we see this kind of question in an exam, if we’re not familiar with the fraction, we’ll check the options to look for the most complicated. We’ll look for decimal. We’ll look for x. We’ll look for a complicated answer. But in reality, the answer is 4 or 1 or 0. Because when I took the exam, that’s what happened, okay? So that is why I’m teaching all of these
to you. So make sure that you understand this in time for the exam. If you have to watch it again, do it. Hit pause when I tell you to do so and answer the
activities to solidify the concepts to you. I also post
questions on Facebook page, make sure that you follow that, okay? All right, I hope you learn something new today. If you did, click thumbs up and make
sure that you share this video with your friends especially if you you’re friends will also take the exam. And if you have a copy of the workbook,
make sure that you answer all the exercises below to solidify your learning. If you don’t have a copy of this workbook yet, and you
want one you can go to www.facebook.com/team to find out how you can get copy of your own, also we’re going to use this same workbook for the live review event. So if you want to know when those are going to
happen and where, you can go to the Facebook page as well. Thank you guys and make sure that you subscribe to this channel, hit the thumbs up, hit the bell
icon so you will be notified as soon as a new video posts. We’re going to
talk about Equalities next. So in order for you to catch that, make sure
you’re subscribed so as soon as I posted it, you’ll see it right away. Thank you guys. Happy learning. Aja! Aja! You can do it. God Bless in your exam. See you in my next video.

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    A-Ann Hinanay

    Thanks po Ms. Lyqa. NGANGA ako nung nag try akong sagutin sa workbook yung may mga fractions. 😀 😀 😀 At least ngayon gets ko na. Woo~

    P.S. uulit ulitin ko talaga 'to para magets ko. Medyo nakakalito pa po apg sinasagutan ko na sa workbook.

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    dong timtim cfd

    sa negative exponent babagsak lang ang concept. kapag negative babagsak because "You become what you believe." Kaya think positive lang tayo AJA AJA. Thanks Mam Lyqa…

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    Raymond Abdon

    ma'am tanong ko lang po kung anu ang sagot dito sa problem.
    (−7)² + (−7²) = ?
    salamat po in advance. more power and god speed

    #teamlyqa

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