Video: Comparing the Values of Exponents by Evaluating Them

Which of the following is a power whose value is greater than 196? [A] 17² [B] 14² [C] 13² [D] 2⁶ [E] 5³

08:21

Video Transcript

Which of the following is a power whose value is greater than 196? We got A) which is 17 squared. B) is 14 squared. C) is 13 squared. D) is two to the power of six. Or E) is five to the power of three.

So what I’m gonna do is work them each out to see what their value is. I’m gonna start with A, 17 squared. Well, 17 squared is equal to 17 multiplied by 17. That’s what it means when it’s a power of two or squared. What I’m gonna do is demonstrate different ways to carry out our multiplications. So for this one, 17 multiplied by 17. And we’ll use the column method. So first of all, what I’m gonna do is multiply seven by each of the values one and seven from the 17 above. So first of all, I have seven multiplied by seven, which is 49. So I put nine in the units column and carry the four into the tens column. Then I have seven multiplied by one, which is seven. Then we add the four that we carried gives us 11. So we have one in the tens column and one in the hundreds column. So great. We’ve multiplied 17 by seven. Now we need to multiply by the one or the ten part of the second value.

Well, with this, what we do is we begin by putting a zero. And the reason we put a zero in the unit column is because we’re multiplying by a 10. So therefore, we won’t have any unit values. Then I’m gonna do one multiplied by seven, which is seven. Well if we think about it. It’s 10 multiplied by seven, which is 70. And that’s why I put seven in the tens column. And then, we’ve got one multiplied by one, which is just one. So we put one in the hundreds column. And if we think about it, that sounds right, because we had 10 multiplied by 17, which is 170. Okay, great. So now what we need to do is add these two values together. So if we add nine and zero, we get nine. One and seven we get eight. And one and one we get two. So therefore, 17 multiplied by 17 is equal to 289. And this is greater than 196. So therefore, A looks like it’s gonna be the answer to our question. But what we’re gonna do is double check by going through each of the values to find out what their value is.

So then we move on to B. And B is 14 squared, which is equal to 14 multiplied by 14. And to work out 14 multiplied by 14, I’m gonna demonstrate a different method. And this is the grid method. So what we have is we split up our 14 into its tens and units. We have 10 and four, 10 and four. So then we multiply 10 by 10 and put it in the top left box. It’s gonna be 100. We’ll think about this is just easy because we know that 10 multiplied by 10 is 100. But if we had a different value, what we can do is multiply the two digits at the start. So in this case, one multiplied by one. And then we see how many zeros there are. There are two. Okay. So we move along to the top right box. 10 multiplied by four is 40. Then box from the left, four multiplied by 10 is 40. And finally, four multiplied by four is 16.

So great. We’ve multiplied all the values. Now, what we need to do is to add them all together. So now if we have 100 add 40 add 40 add 16, I’ve lined up in a column. We’d have six in the units column. Then, we’ve got four add four add one is nine. So that’s nine in the tens column and just one for the hundreds column. So therefore, we get 196. Well, if we check back, we can see that the question asked for a power whose value is greater than 196. However, we’ve calculated that 14 squared is equal to 196. So therefore, this is not going to be the answer to our question.

So now what we’re gonna do is move on to C. And that is 13 squared, which is 13 multiplied by 13. And once more, I’m gonna show a different method. And this method is also known as the diagonal method or Chinese multiplication. So for this, what we’re gonna do, first of all, we’re gonna look at the top left box. And we’ve got one multiplied by one. And the answer is just one. So what we do is put zero in the top half of the box. And this is our tens area. And we put a one in the bottom right part of the box. And this is cause it’s our units area. Then we do the same to the top right. Where we put zero, three cause three multiplied by one is three. Bottom left is also zero, three. And then finally, bottom right is zero, nine cause three multiplied by three is nine.

So now what we do is we add along our diagonals. So we can see for the first diagonal we’ve just got nine. And then the next diagonal, we have three add zero add three, which is six. And the next diagonal is just one. And then, the final diagonal is zero. So therefore, we can say that 13 multiplied by 13 is 169. And we get this from just reading round. And this is less than 196. So C is also not the correct answer. It’s worth noting that we could’ve also worked out 13 multiplied by 13 using a mental method. Because we could’ve had 13 multiplied by 10 is 130. And then we’ve got three multiplied by 13 will be 39, which gives us our 169. Okay, great. Now let’s move on to D.

Well, for D, we have two to the power of six. And this is equal to two multiplied by two multiplied by two multiplied by two multiplied by two multiplied by two. Okay, so let’s work this out. Well, there’s a couple of ways we could work this out. First of all, we could split it into pairs. And we could do two multiplied by two multiplied by two multiplied by two multiplied by two multiplied by two. So this will be four multiplied by four multiplied by four. Well then, we know that four multiplied by four is 16. So this would be 16 multiplied by four. And this would be 64. And that’s because if we have 16 multiplied by four, four sixes are 24. So we’d have four in the units column and two in the tens column if we did it using column multiplication. And then, four times 10 is 40. So we add them together. And we get 64. Well, two to the power of six is equal to 64 as we just found out. So therefore, this is less than 196. So D will not be the correct answer.

As I said there would’ve have been another way that we could’ve worked this out. And that would’ve been by doubling five times because we’ve got two. And then we multiply it by two, which is doubling it. And then multiply it by two, which doubles it again, et cetera. So if we start with our two, then double it, it’s four. Then double it again, it’s eight. And again, it’s 16, then 32, and finally 64.

Okay, great. We can move on to the final answer, which is E. And E is five cubed, which is five multiplied by five multiplied by five. Well, five multiplied by five is 25. So then we get 25 multiplied by five. Again, we could work this out in various ways. But one method would be to say that four multiplied by 25 we know is 100. Then we have one more. So we add that onto 100, which gives us 125. Or again, with another mental method, we could’ve done five multiplied by two is 10. So five multiplied by 20 is 100. Five multiplied by five is 25. Add them together, we get 125. Well, 125 again is less than 196. So E is not the correct answer. So we can confirm the correct answer is answer A. And we can say that the power whose value is greater than 196 is 17 squared.

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