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What is the units digit of (13)^4(17)^2(29)^3? (A) 9 (B) 7

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What is the units digit of (13)^4(17)^2(29)^3? (A) 9 (B) 7 [#permalink] New post 07 Apr 2006, 04:54
What is the units digit of (13)^4(17)^2(29)^3?

(A) 9

(B) 7

(C) 5

(D) 3

(E) 1
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Andre Crompton
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 [#permalink] New post 07 Apr 2006, 05:06
Answer E...

3*3*3*3= units digit 1

7*7= units digit 9

9*9*9= units digit 9

So....

9*9*1= units digit 1.
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 [#permalink] New post 07 Apr 2006, 05:11
3^4 = 81
7^2 = 49
9^3 = 729

Units digit = 1*9*9 = 1
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 [#permalink] New post 07 Apr 2006, 05:59
clever ! thanks guys :) good thing to know. i had a question like this, took me a little while to do it my own ( not soo clever ) way

if lets say you had 2 find the 10's or 100's digit how would you do it ? would the same pattern work ?
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 [#permalink] New post 07 Apr 2006, 08:26
NTLancer wrote:
if lets say you had 2 find the 10's or 100's digit how would you do it ? would the same pattern work ?


Yes, it all depends on the number. You just have to learn the cycle
for example:
7^100 -
7^2 -.9
7^3 -.3
7^4 -.1
7^5 -.7
------
See the pattern, 7^..5 always has 7 unit digit.
7^10 -.7
------
7^50 -.7
------
7^100 -.7
  [#permalink] 07 Apr 2006, 08:26
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What is the units digit of (13)^4(17)^2(29)^3? (A) 9 (B) 7

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