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# If (4^2)^3*2^6=2^y, what is the value of y?

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Manager
Joined: 20 May 2014
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Kudos [?]: 30 [0], given: 163

If (4^2)^3*2^6=2^y, what is the value of y? [#permalink]  11 Nov 2017, 23:59
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If (4^2)^3*2^6=2^y, what is the value of y?

(A) 6

(B) 12

(C) 18

(D) 36

(E) 72

Kudos for correct solution.
[Reveal] Spoiler: OA
Director
Joined: 03 Sep 2017
Posts: 522
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Kudos [?]: 195 [0], given: 66

Re: If (4^2)^3*2^6=2^y, what is the value of y? [#permalink]  12 Nov 2017, 23:22
Let's use the properties of exponentials, i.e. the fact that that (x^a)^b = x^{ab} and x^a x^b = x^{a+b}.

In our case, we can rewrite the left-hand side of the equation as (4^2)^3 = ((2^2)^2)^3 = 2^{12} and then 2^{12}2^6 = 2^{18}.

Re: If (4^2)^3*2^6=2^y, what is the value of y?   [#permalink] 12 Nov 2017, 23:22
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