Video: AQA GCSE Mathematics Foundation Tier Pack 4 • Paper 3 • Question 4

Work out 512 as a power of two. Circle your answer. [A] 2⁵ [B] 2⁷ [C] 2⁹ [D] 2¹¹

02:25

Video Transcript

Work out 512 as a power of two. Circle your answer. The options are two to the power of five, two to the power of seven, two to the power of nine, or two to the power of 11.

Well, let’s first take a look at two to the power of five. Well, two to the power of five means two multiplied by two multiplied by two multiplied by two multiplied by two. So you can see that it’s there five times. Well, due to the nature of multiplication, we can do it in sections if we’d like. So we can see that two multiplied by two is four and two multiplied by two is four. So therefore, we’re gonna get four multiplied by four multiplied by two. So therefore, we’re gonna get 16 because four multiplied by four is 16 multiplied by two. So it gives a total of 32. So we can say that two to power of five is 32. And we could’ve also done this on our calculator.

Well, if we consider two to the power of seven. Well, two to the power of seven is just two to the power of five multiplied by two to the power of two because it’s two to the power of five multiplied by two multiplied by two. So therefore, it would just be 32 multiplied by four. And that’s because 32 was two to the power of five. Then multiply this by four cause two squared is four. So therefore, this gives 128. And what we can see is that as we move from the powers of two that we have, so what we we’re doing is increasing the power of two by two each time, so from two to the power of five, two to the power of seven, two to the power of nine et cetera. We multiply by four.

So if we multiply 128 by four, we get 512. Again, we can just do that on the calculator. But if you want to do it separately, you could do four multiplied by 100 which is 400. Four multiplied by 20 which is 80. So you’d have 480. And then, four multiplied by eight is 32. Well, if you add 32 to 480, you get 512.

So therefore, the correct answer is two to power of nine. So we can say that 512 as a power of two is two to the power of nine. And if we want to find out what the final power was equal to, we can see that two to the power of 11 multiplied by four gives us 2048.

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