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

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

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Re: If (4^2)^3*2^6=2^y, what is the value of y? [#permalink] New post 12 Nov 2017, 23:22
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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 \(2^{12}2^6 = 2^{18}\).

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

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