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# What is the units digit of [m](3^70)(7^71)[/m]?

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Re: What is the units digit of [m](3^70)(7^71)[/m]? [#permalink]
Cyclcity of 3 : 3,9,7,1
Cyclicity of 7 : 7,9,3,1
3^50 unit digit :9
7^52 unit digit : 1
9*1:9
Option E

BrentGMATPrepNow wrote:
What is the units digit of $$(3^{50})(7^{52})$$?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9

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Re: What is the units digit of [m](3^70)(7^71)[/m]? [#permalink]
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Archit3110 wrote:
Cyclcity of 3 : 3,9,7,1
Cyclicity of 7 : 7,9,3,1
3^50 unit digit :9
7^52 unit digit : 1
9*1:9
Option E

Nice work!
Can you also spot a shortcut that helps us answer the question in 10 seconds?
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Re: What is the units digit of [m](3^70)(7^71)[/m]? [#permalink]
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BrentGMATPrepNow
Another way is

3^50*7^50*7^2
For
3^50*7^50 unit digit is 1 and 7^2:unit digit 9
1*9;9 option E

BrentGMATPrepNow wrote:
Archit3110 wrote:
Cyclcity of 3 : 3,9,7,1
Cyclicity of 7 : 7,9,3,1
3^50 unit digit :9
7^52 unit digit : 1
9*1:9
Option E

Nice work!
Can you also spot a shortcut that helps us answer the question in 10 seconds?

Posted from my mobile device
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Re: What is the units digit of [m](3^70)(7^71)[/m]? [#permalink]
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Top Contributor
BrentGMATPrepNow wrote:
What is the units digit of $$(3^{50})(7^{52})$$?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9

Useful property: $$(x^k)(y^k) = (xy)^k$$

First rewrite the given expression as follows: $$(3^{50})(7^{52})=(3^{50})(7^{50})(7^{2})$$

Apply the property to get: $$(3^{50})(7^{50})(7^{2}) = (3 \times 7)^{50}(7^{2})$$

Evaluate: : $$(3 \times 7)^{50}(7^{2})=(21)^{50}(7^{2})$$

Since $$21^n$$ has units digit $$1$$ for ANY positive integer $$n$$ we can write: $$(21)^{50}(7^{2}) = (????1)(49) =$$ ?????9

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Re: What is the units digit of [m](3^70)(7^71)[/m]? [#permalink]
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Re: What is the units digit of [m](3^70)(7^71)[/m]? [#permalink]
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