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# From a Kaplan Practice Test: What is the units digit of

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Intern
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From a Kaplan Practice Test: What is the units digit of [#permalink]  03 Jul 2006, 07:33
From a Kaplan Practice Test:

What is the units digit of (9)^5 * (10)^3 *(7)^3?

Their explanation skips several steps. Could someone please explain the quickest way to solve this problem?
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Manager
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peachtree wrote:
From a Kaplan Practice Test:

What is the units digit of (9)^5 * (10)^3 *(7)^3?

Their explanation skips several steps. Could someone please explain the quickest way to solve this problem?

9^2 = 81
9^3 = 729
9^4 = 6561
9^5 = 59049
You see the pattern where 1 and 9 switches back and forth for the unit number.

10^3 = 1000 with a unit number of 0
7^3 = 343 with a unit number of 3.

But when we are multiplying all three, it should jump out you that you are going to multiply by 9*0*3. Therefore the unit number is 0.
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if the question was 9^5 * 13^3 * 7^3?

(sorry I typed it incorrectly the first time.)

i get what you're saying though: to look for a pattern.

in the kaplan answer, they said to think of (13)^3*(7)^3 as (13*7)^7.
Does that make sense to you?
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peachtree wrote:
if the question was 9^5 * 13^3 * 7^3?

(sorry I typed it incorrectly the first time.)

i get what you're saying though: to look for a pattern.

in the kaplan answer, they said to think of (13)^3*(7)^3 as (13*7)^7.
Does that make sense to you?

I am kind of confused...
(13)^3*(7)^3 = 753571
(13*7)^3 = (91)^3 = 753571
(13*7)^7 = (i cheated and used the calculator) = 51676101935731

only the unit number matches. By any change is the (13*7)^7 a typo and needs to be (13*7)^3? if it is a typo, I get it, if not... I am not sure...but one of the Math guru will post a response...
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I thought it must have been a typo too. Thanks for your help!
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Quickest way would be find unit digit of each term by taking only the unit digit:

Unit digit of 9^5 = 9
Unit digit of 13^5 (Consider only 3 instead of 13) = 7
Unit digit of 7^3 = 3

Now unit digit of multiplication of 9, 7 and 3 = 9
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peachtree wrote:
From a Kaplan Practice Test:

What is the units digit of (9)^5 * (13)^3 *(7)^3?

Their explanation skips several steps. Could someone please explain the quickest way to solve this problem?

9^5 = 3^(2*5) = 3^10 ..pattern is 9,7,1,3,9,7,1,7,9.. so ends with 9

13^3 -> ends with 7, (3*3*3)

and 7^3 ends with 9*7->3

so the final number would end with 3*9*1 ->7
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