what is the answer to 48 in a factor tree using exponents?
84784
You should really just draw out the factor tree.\n\nYou will get 2power4 times 3 in prime factorization.\n\nYou just find the lowest prime number and a multiple and branch down the tree in the same process. Also bring down the primes. Once you have all prime numbers you put them together them to get the prime factorization.\n\nHere is the tree:\n\n                             48\n                            /  &#92;\n                           2 * 24\n                          /   /  &#92;\n                         2 * 2 * 12\n                        /   /   /  &#92;\n                       2 * 2 * 2 *  6\n                      /   /   /    / &#92;\n                     2 * 2 * 2  * 2 * 3\n\n                             2^4 * 3
911082
logx+log(x+48)=2\n=>log{x(x+48)}=2\n=>log(x^2+48x)=2\n=>x^2+48x=10^2\n=>x^2+48x-100=0\n=>x^2+50x-2x-100=0\n=>x(x+50)-2(x+50)=0\n=>(x+50)(x-2)=0\nhence,\nx=-50 or x=2
239852
Use the guess and check method.\n\nFirst, find all the factors of the number at the far right (example: in the 1st exercise, it is 25, so...\n\n25=1*25, 5*5\nNext, find those factors that together add up to the number in the middle.(10, in this case) . That would be: 5*5=25 and 5+5=10. So you write...\n(a+5)(a+5). \nDo this with all the rest.However, this sadly doesnt work with trinomials that have its largest exponent be bigger than 2. Also the term with the largest exponent (remember:it has to be 2) cannot have a coefficient.\n\nNote:this method works with the following exercises:1,2,3,4,5,6,and 7. I'm pretty sure. :)
420710
I know it has already been answered but I"ll take a chance with something different. Ok 3 to the third power plus two would be 3 to the fifth power which is 243.\n :)
343166
12.\nPrime factorization of each number:\n               \n60= 2x2x3x5\n84= 2x2x3x7\n    \n60 and 84 share the prime factors of 2, 2 and 3. So, you multiply those together to get 12.
222065
nCr = n!/(n - r)!r!\n\nWhere\nx! = x(x - 1)(x - 2)(x - 3)... 1\nExample\n7! = 7*6*5*4*3*2*1 = 5040\nx! reads "x factorial"\n\nso,\n5C4 = 5!/(5 - 4)!4!\n= 5*4*3*2*1 / [1!(4*3*2*1)]\n= 120/1(24)\n= 120/24\n= 5
652953
I got:\n1. 6x^2 - 36x +48\n2. 6x + 22
853291
4 is the answer. Here's how:\n4 appears after a break of two numbers, so the number that follows 40 must be 4
781458
if half yx is 24 then yx is 48\n\nso y = 48/x
899336
84, without even needing to check. That is 2*2*3*7, which gives 3 prime factors. You can't get 4, since 2*3*5*7 is too big.
56508
first, do 2 to the 12th power (exponents take precedent over multiplication) which is 4096. Then multiply that by 86 and get 352256.  It's quite simple, really.
483565
the factors of 27 are 3-3-3.  when you have two of the same number in a factor tree, you can take them outside the root.  So now you have 3squareroot3.  squareroot3 + 3squareroot3 = 4 squareroot 3.  Make sense?
375926
The last digit of the powers of 2 follow a definite pattern, which is 2, 4, 8, 6, and then again 2, 4, 8, 6 etc. \n\nTo find the answer, simply take 51 mod 4, (which happens to be 3), and the third number in the list is 8. The answer is therefore 8.
543957
The answer is 480. You can go to Progams, then Accessories, and then calculator.\n\nOr, you can multiply 24 times 2 which is 48 and add a zero to the end so it becomes 480
15502
35\n  16\n+ 47\n____\n  98\n+  2\n____\n 100
83369
I am giving you a method which would minimize number of possibilities.\nFactorize the number of factors( in your example 9) in as many way as possible.( in your example 9 and 3*3)\nNow find out the possible numbers ( one for one factor combination) in following way ( we are going to have 2 numbers)\nThen all factor combinations are sorted so that largest one is in first place and lowest one in last place.\nFor a factor combination x1*x2*x3*...xn*...\nthe number will be \n2^(x1-1) * 3^(x2-1) * 5^(x3-1) * ... * pn(xn-1)...\nwhere pn is nth prime number.\nFor our two combinations,\nfor 9-> 2^(9-1)=256\nfor 3*3-> 2^(3-1) * 3^(3-1) = 36\nLowest of these numbers is our result. \nIn our example it is 36.\nLet us see another example lowest number with 12 factors.\n12 factorizes to 12, 4*3, 6*2, 3*2*2\nfor 12-> 2^(12-1)=2048\nfor 4*3-> 2^(4-1) * 3^(3-1) = 72\nfor 6*2-> 2^(6-1) * 3^(2-1) = 96\nfor 3*2*2-> 2^(3-1) * 3^(2-1) * 5^(2-1)=60.\nSo our answer is 60.\nThis method will be if the number of factor cobination  is too large. An way to get good answer( may not be correct) is to start from prime factorization and continue untill collecting first two terms into one causes better result.\n\nThat is in case of 12\nWe will start from 2*2*3 and get 60.\nThen test if 4*3 is better. If not we will take 60 as answer.( as it is 72 so we will).\nThis case we have correct result but modified version may not produce correct result.
535646
I think you mean 36 not 38 since\n\n4 = 4*3^0\n12 = 4*3^1\n36 = 4*3^2\n108 = 4*3^3\n324 = 4*3^4\n\nSo, if that's the case, it's 324.\n\nUPDATE: Kemmy, 1^3+1 = 2, not 4.