Subject: studdent from Australia, yr 12 (final year)

hello. i am kylie mcalpine and a final year student in Perth, western australia. i was told about this webstie so i decided to ask for your assistance in and investigation i am currently doing at school

there are 3 tables

the other 2 tables included are n to the power of 7, n being 1-10 and the other is 4 to the power of n i have figured out the patterns for the tables, the last digits in the table of 3 forms a continuos pattern of 3,9,1,7

the other tables have patterns as well. table 7 has the pattern of 7,,9,3,1 and table 4 has the pattern of 4,6,4,6 etc.

the questions we have been asked are what is the units digit of the following:

a) 3⁵⁸
b) 23⁵⁸
c) 17³¹

and the harder question of:

what is the units digit of the following sum: 13⁸⁴¹ + 17⁵⁰⁸ + 24⁶¹⁷ = ???????

if there is any information i have not included, please inform me.

thankyou again
kylie

Here is an outline of how to do it:
In the 3 to the power of n table, the pattern can be developed without calculating each power:

The pattern repeats every four digits.

Imagine that you complete this table to 58 rows. 58/4 = 14 with a REMAINDER 2 so the pattern repeats 14 times and then there are two more rows with 3 and 9 in the units digit column. Thus the units digit of 3⁵⁸ is 9.

Using the same technique you can complete the next two problems.

For the harder question use the above technique to find the units digit of each of 13⁸⁴¹, 17⁵⁰⁸ and 24⁶¹⁷.