Write √ 128 as a power of 2 ?

After a bit of research I can see that in most cases this question means to present your answer as TWO to the power of something. (when expressed 'as a power of two') It can be tricky when we also hear 'TO the power of 2' or 'power 2'. In this case, 128 can be broken down into 2 multiplied by itself 7 times, AKA: 2 TO THE POWER OF SEVEN 2^7 add back in the Sq root. √(2^7) as i mentioned before, this can be written as (2^7)^0.5 Using the multiplication of exponents in brackets rule (x^m)^n = x^mn, We can multiply the powers together (the one inside the bracket and the one outside) so: (2^7)^0.5 2^(7x0.5) So in this case your answer would be 2^3.5

Joshua Mosiuk

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Maths Tutor • Secondary

Hi Oliwia, not sure if we are missing some information to complete this question, but I can share a couple of things that may help: Any square root can be expressed as a power of 1/2, in this case: √ 128 = 128^1/2 - though I think you want your answer expressed to the power of 2, not to the power of half. If you were looking to have an answer that was to the power of 2, you may need to first solve √128, which is 11.31. If you want to express 11.31 as a power of 2, you would need to find the square root of this. √11.31 = 3.36 3.36^2 is likely to be your answer based on the wording of your question. Also note that we found out the square root of a square root, this doesn't mean we found the cubed root, and because we did this in stages, it would not work to reverse the calculations to get our original number. Hope this helps!

Joshua Mosiuk

634 students helped

Maths Tutor • Secondary

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