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

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Senior Manager
Joined: 20 May 2014
Posts: 282
Followers: 15

Kudos [?]: 49 [0], given: 220

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

100% (00:19) correct 0% (00:00) wrong based on 2 sessions
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: 521
Followers: 1

Kudos [?]: 334 [1] , given: 66

Re: If (4^2)^3*2^6=2^y, what is the value of y? [#permalink]  12 Nov 2017, 23:22
1
KUDOS
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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