Is 2^3^2 = 64 or 512? I have a Casio fx-115MS calculator that calculates it left to right and gives me 64 and my TI-92 plus calculator apparently does this from right to left and gives me 512.
2006-07-09 18:45:57 · 9 answers · asked by Michael M 6 in Science & Mathematics ➔ Mathematics
I understand how it works if I add parentheses.
I’m just a little shocked that my TI-92 performs the equation from right to left which seems backwards to me.
2006-07-09 19:01:11 · update #1
In the absense of parentheses, one should always evaluate repeated exponents from right to left (or as I like to think about it, from top to bottom). So, for instance,
2^3^4^5 = 2^(3^(4^5))
or in your case,
2^3^2 = 2^(3^2) = 2^9 = 512.
The way you might think about it in your head is the following:
Hmm, 2^3^2. Reading left to right, I have to raise 2 to a power. What power? The power is 3^2 = 9. Ahh, so 2^3^2 = 2^9.
2006-07-10 06:18:14 · answer #1 · answered by Anonymous · 6⤊ 1⤋
Well, I'm not a math major or anything, but I did take a couple math courses in college. It really depends on exactly how you mean that set right there...
(2^3)^2 would be...
(8)^2 = 64
But, if you mean it this way 2^(3^2) that would be...
2^(9) = 512
If you have the base number 2 with a super script 3 above it and above that is another little super script 2, (will attempt to format this to look right....)
2
3
2
If it looks something like that, then start at the top, do the 3^2 first, giving you this:
9
2
which would end up being 512.
Thats how I understand it, and written exactly as you have it above in the question, I read that as this last example.
Final answer, 512.
(Sorry if my answer is sloppy)
2006-07-10 01:52:14 · answer #2 · answered by guardianlegend01 2 · 0⤊ 0⤋
It's 512. It's that because if it was 64 the equation would have to be (2^3)^2.
2006-07-10 03:31:29 · answer #3 · answered by Eric X 5 · 0⤊ 0⤋
It's generally accepted that algebraic expressions are evaluated by order of operations and then interpreted from left-to-right for operations of equal priority (at least, in the Western world); thus, the answer is usually 64. However, some symbolic calculators appear to give higher priority to simplification of powers. Maxima (or Macsyma), AMS, and HP-49 all produce the answer 512.
2006-07-10 03:02:10 · answer #4 · answered by Tetris Otaku 3 · 0⤊ 0⤋
it's 512, you do 3^2 which is 9, then 2^9
2006-07-10 01:47:11 · answer #5 · answered by Jim2386 3 · 0⤊ 0⤋
both are correct in some sense, it depends what the question is,
(2^3)^2 is actually 2^(3*2), where as 2^(3^2) is 2^9. so both your calculator are correct with whatever logic they have.
in either case the order has to be right to left, with proper understanding of parenthesis, in absence of parantheiss, the answer of your question has to be 2^9
2006-07-10 01:50:48 · answer #6 · answered by plzselectanotherone 2 · 0⤊ 0⤋
Is 2^3^2 =
a. (2^3)^2 = (2*2*2)^2 = 8^2 = 64
b. 2^(3^2) = 2^(3*3) = 2^9 = 512
put in the order of precedence.
2006-07-10 01:58:36 · answer #7 · answered by calpal2001 4 · 0⤊ 0⤋
It's (2^3)^2
Or, using the properties of exponents, when you have one exponent to another, just multiply, so this is equal to 2^6, which is 64
2006-07-10 01:48:13 · answer #8 · answered by Amber E 5 · 0⤊ 0⤋
(P.E.M.D.A.S) Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction. That is the proper order.
2006-07-10 01:49:09 · answer #9 · answered by Brandon 2 · 0⤊ 0⤋