This SAT question was given in exam and everyone got it wrong | Algebra
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- Опубліковано 26 вер 2024
- What is the correct answer? What do you think about this problem?
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✓{(4)^4}^4 is the towering entity under sq. root. After taking sq. root the entity comes to {(4)^4}^2 . As such,(C) is the correct answer not (D).
Powers are right associative, so I calculate 4⁴ and get 4^256. The square root of that would then be 4^128. So it is the same as 4^2^7. 👍🏼
I would say d. 4^4 = 2^8 . (4^(2^8))^1/2 = 4^(2^7). the exponent is 256 and you divide it by 2, get 128, which is 2^7.
I must be a math geek because I done with college math but I find myself gravitating to these math videos just for the helluva it.
It is a hard problem because you need to know the convention of how to interpret a^b^c. By convention you start at the top, a^(b^c ) but if you didn’t know that it is natural to assume you should start at the left (a^b)^c
4^4 is (by simple arithmetic) 256 then divided by 2 is 128. So answer is 4^128. When I then looked at your answers I saw it had to be in exponential form, so, again simple arithmetic:128 =2^7.
It depends on how you group the calculation of the powers. Sqrt((4^4)^4)=65536=Answer c. So what is teh definition of 4^4^4? Is it (4^4)^4 or 4^(4^4)? The results are extremely different. After you take the sqrt of the second, the result is 4^128 = 1.58x 10^77.
You are indeed correct. Result C is correct. The speaker has made a notational error. I have explained his error in a detailed comment. If you cannot find it, let me know and I'll post it also as a reply to your comment.
If this really was a question in an exam, it doesn't say much for the teacher.
I had 2^(4^4) which has the same value as 4^(2^7).
A very easy question that most students could solve mentally in less than 15-seconds.
Really ?
Also 2^2^8
Answer d, because this root is equal 4^128, and 128=2^7.
I'm getting c. 4 to the fourth power, squared. or 4 to the eighth. or 65,536. I've gone over my work again and again and can't find where I'm wrong. But since the three posters ahead of me all agree that it is D. I'll entertain the idea that I'm the problem.
Here's how I checked my work. 1. Via calculator: Ignore the radical sign here for a moment 4^4^4 = 4,294,967,296. Now apply the radical sign and take the square root. You get 65,536. Now look at C. 4^4^2 = 65,536. As does 4^8.
2. Going back to the original problem, isn't 4^4^4 = 4^16? Then taking the square root means you have 4^8?
i'll confess to not playing with exponents regularly but I thought I was on solid mathematically logical ground here. What am I missing ?
You calculated 4^(4*4)= 4^16= 4294967296. The problem calls for a calculation of 4^4^4= 4^256.
You are indeed correct. Result C is correct. The speaker has made a notational error. I have explained his error in a detailed comment. If you cannot find it, let me know and I'll post it also as a reply to your comment.
@@spondulix99 Thank you spondulix99 Your detailed comment is the clearest explanation of the nuance of this issue I have seen. You should be a teacher.
The problem is your step, 2 4^4^4 equals 4^256 and the square root is 4^128
(4^(4+4+4+4))^1/2= 4^8. Answer is C.
Hic est 4^128 responsum.
I can only assume the students had been badly taught.
C
4?
Error
The correct answer is c), and not d). The error made by the speaker follows from failure correctly to understand which part of 4^4^4 plays the role of the exponent. He incorrectly takes the right-most two 4s as the exponent of the remaining left-most 4. That is, he takes 4^4^4 to be 4^(4^4). This is not correct, and is a commonly made mistake.
The universally recognized and accepted meaning of x in the notation A^x, is that x is the power to which A is to be raised, where A is any constant or expression. When no parentheses are introduced to indicate otherwise, x stands for the fully evaluated scalar power to which A is to be raised. If the exponent x is itself of the form B^y, then parentheses must be placed around B^y to direct that B^y must first be evaluated in order to determine the power to which the constant or expression A is to be raised. Absent any such parentheses, as in this problem, the universally accepted interpretation is that the exponent in an expression such as a^b^c^...^x^y^z is the right-most fully evaluated scalar power to which the sequence to its left is to be raised.
In this case, f = sqrt(4^4^4) = sqrt((4^4^)^4) = (4^4)^(4/2) = (4^4)^2 =256^2 = 65,536.
That is, delineated result c) is the correct expression of 4^4^4.
9 = 3² -> you do not apply the same rules in the 2nd example - 3rd root of 9 ...
Let 4⁴ be A and take sqrt of A⁴ -> answer c...
C