exponent problem TEST TOMMORROW HELP PLZ

[lunarskull]

hi,
i have a test 2morrow, and i have to know how to find exponents
the problem is:
What is the last digit in the number 7^1000 (you must show all work)

so can someone show me how to do this problem without just typing it into the calculator??

some help wud b greatly appreciated

 

[stapel]

What is the last digit of 7⁰?
What is the last digit of 7¹?
What is the last digit of 7²?
What is the last digit of 7³?

Keep going until you see a pattern.

Eliz.

 

[lunarskull]

im sorry, but im couldnt see a pattern.
7^1- 7
7^2-49
7^3- 343
7^4- 2401
7^5-16807
7^6- 117649
7^7- 823543
7^8- 5764801
7^9-400353607
7^10- 282475249

ok so the pattern goes 7,8,3,1, does that mean the answer is 7??

 

[stapel]

Where does the exponent "1000" fall in that pattern?

Eliz.

 

[pav]

isnt 7^1000

((7^10)^10)^10)

 

[stapel]

isnt 7^1000 ((7^10)^10)^10)

Yes, but that doesn't answer the question. Where, in the listing I started, showing the pattern of final digits, does "1000" fall? I didn't ask about powers of ten; I asked about the powers 0, 1, 2, 3, 4, ... and the corresponding last digits 1, 7, 9, 3, 1, 7, 9, 3,... Where, in the "1, 7, 9, 3" cycle, does the power "1000" fall?

Eliz.