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

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Joined: 02 Sep 2009
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If (4^2)^3*2^6=2^y, what is the value of y?  [#permalink]

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12 Nov 2017, 01:00
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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

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

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12 Nov 2017, 08:57
Bunuel wrote:
If $$(4^2)^3*2^6=2^y$$, what is the value of y?

(A) 6

(B) 12

(C) 18

(D) 36

(E) 72

$$(4^2)^3*2^6=2^y$$

or, $$((2^2)^2)^3*2^6=2^y$$

or $$2^{12}*2^6=2^y$$

so $$2^{12+6}=2^y$$

or $$2^{18}=2^y$$, hence $$18=y$$

Option C
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If (4^2)^3*2^6=2^y, what is the value of y?  [#permalink]

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12 Nov 2017, 08:59
Bunuel wrote:
If $$(4^2)^3*2^6=2^y$$, what is the value of y?

(A) 6

(B) 12

(C) 18

(D) 36

(E) 72

$$(4^2)^3*2^6=2^y$$
$$(4^6)*2^6=2^y$$
$$((2^2)^6)*2^6=2^y$$
$$2^{12}*2^6=2^y$$

Bases are the same. Set exponents equal; for multiplication, add exponents.

(12 + 6) = y
y = 18

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If (4^2)^3*2^6=2^y, what is the value of y? &nbs [#permalink] 12 Nov 2017, 08:59
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