3,127.
5x5x5x5x5
The answer is 3125. (5x5x5x5x5)
ok. I had this same question! Nut the answer is 5^5... 5x5x5x5x5
5*5*5*5*5 = 55 = 3125
5x5x5x5x5 = 5x5 = 25 x 5 = 125 x 5 = 625 x 5 = 3125
If digits can be reused, then 5x5x5x5x5 = 3125. If digits cannot be reused, then 5x4x3x2x1 = 120.
20 is the answer in standard form because 5x5x5x5 is 5x4 but with four fives.
An exponent means "this many times." So, 4 cubed (to the power of 3; a 3 exponent.) is 4 NOT times 3, but 3 TIMES. So it is 4x4x4(=64). Or, 5 to the power of 5 is 5 times itself 5 times, so, 5x5x5x5x5(=3,125). 3 to the power of 9 is 3 times itself 9 times. Basically, the exponent tells how many times you multiply the number by itself. Does that help?
a to the b power means b lots of a, all multiplied together. Thus 5 to the 5 power or 55 is 5x5x5x5x5, and 5 to the 3 power, or 53 is 5x5x5. Thus the question can be written as 5x5x5x5x5x4x5x5x5x6. This is now a simple calculation that comes out at 9,375,000. Thus 5 to the 5 power times 4 times 5 to the 3 power times 6 is 9,375,000.
5^(5) / 5^(4) = 5^(5-4) = 5^(1) = 5 or 5^(5) /5^(4)= 5x5x5x5x5 / 5x5x5x5 Cancel down by '5' ( top and bottom) and we are left with 5/1 = 5 as before. NB We do normally show number to the power/exponent of '1' except to aid in exponential calculations.
We first make an assumption that you are picking 5 letters from 26. If this is not the case, the problem is different. This is covered at the end of the answer. With repetition allowed (letters can be re-used), and order is not important since it is a combination (not a permutation), it is (26+5-1)!/(5!)(26-1)! This is a really big number! If it were a permutation with repetition, this is the same as the number of ways to pick 5 things from 26 with replacement. There are 26 choices for each letter, so you have 26x26x26x26x26 permutations. No repetition, order is important, it is 26! / (26-5)! = 26 x 25 x 24 x 23 x 22 = 7,893,600 No repetition, order doesn't matter (ABCDE is the same as EDCBA is the same as CEDAB, etc), it is 26! / (5!(26-5)!) = (26 x 25 x 24 x 23 x 22)/(5 x 4 x 3 x 2 x 1) = 65,780 What if you just have 5 letter already picked. Meaning you are not worried about picking the 5 from the alphabet, you already have 5 fixed letter. Some may be the same letter or not. If you allow for repetition of the letters, you have 5x5x5x5x5 permutations. For combinations, it would be 11!/5!4!=7983360 MOST LIKELY, you just have 5 distinct letters and you want to arrange them where order does matter and you cannnot repeat. In this case you have 5 choices for the first letter, 4 for the second, 3 for the third etc. So you have 5! or 120 choices. Of course if you have 5 things and the order does not matter, there is only 1 way to arrange them. For example. ABCDE is the same as ABEDC. So in dealing with combinations and permuations, the language must be quite exact. A small difference changes the entire problem. See related MathsIsFun link for more information.