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shoonya
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what is the unit's digit of (9)^5 * (13)^3 * (7) ^ 3 in 23 Jul 2006, 20:00
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what is the unit's digit of (9)^5 * (13)^3 * (7) ^ 3

in words, what is the unit digit of the product of 9 to the power 5, 13 to the power 3, and 7 to the power 3?



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what is the unit's digit of (9)^5 * (13)^3 * (7) ^ 3 in 23 Jul 2006, 21:38
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It's 9.
9 has a cyclicity of 2.
7 has a cyclicity of 4.
So the last digits are ...9 * 7 * 3 ==> 9
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what is the unit's digit of (9)^5 * (13)^3 * (7) ^ 3 in 23 Jul 2006, 23:24
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9

9^5 will have last digit = 9
13^3 will have last digit = 7
7^3 will have last digit = 3

9*7*3 will have last digit = 9
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Futuristic
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what is the unit's digit of (9)^5 * (13)^3 * (7) ^ 3 in 24 Jul 2006, 00:25
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shoonya
what is the unit's digit of (9)^5 * (13)^3 * (7) ^ 3

in words, what is the unit digit of the product of 9 to the power 5, 13 to the power 3, and 7 to the power 3?
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something to keep in mind for these problems:-

If the last digit of a number is 2,3,7,8, it cycles every 4th multiplication (or power). If the last digit is 9 the cyclicity is 2. If the last digit is 1, 5, 6, the cyclicity is 1. Consider the following example:-

2^1 = 2
2^2 = 4
2^3= 8
2^4 = 16
2^5 = 32 (last digit is 2)
2^6 = 64 (last digit is 4)

basically every 4th power of the number is the same if the cyclicity is 4.

from the above one can infer that the last digit of 2^1099 has the same last digit as 2^3.

In this case, the answer I agree is 9.
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what is the unit's digit of (9)^5 * (13)^3 * (7) ^ 3 in 24 Jul 2006, 03:38
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thanks Futuristic, this is helpful.
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what is the unit's digit of (9)^5 * (13)^3 * (7) ^ 3 in 25 Jul 2006, 03:25
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9

Unit digit of 9^5 = 9 (just consider the unit digit ..... doesnot matter what the other digits are)

Unit digit of 3^3 = 7
Unit digit of 7^3 = 3

Hence final unit digit = 9*7*3 = 9
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what is the unit's digit of (9)^5 * (13)^3 * (7) ^ 3 in 25 Jul 2006, 03:42
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ps_dahiya
9

9^5 will have last digit = 9
13^3 will have last digit = 7
7^3 will have last digit = 3

9*7*3 will have last digit = 9
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gud explanation dahiya...did the same method...



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