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If (4^2)^3*2^6=2^y, what is the value of y?
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11 Nov 2017, 23:59
11 Nov 2017, 23:59
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Question Stats:
92% (00:17) correct
7% (00:00) wrong based on 14 sessions
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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.
(A) 6
(B) 12
(C) 18
(D) 36
(E) 72
Kudos for correct solution.
Re: If (4^2)^3*2^6=2^y, what is the value of y?
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12 Nov 2017, 23:22
12 Nov 2017, 23:22
1
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
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
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Re: If (4^2)^3*2^6=2^y, what is the value of y?
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23 Mar 2022, 12:13
23 Mar 2022, 12:13
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
Kudos for correct solution.
(A) 6
(B) 12
(C) 18
(D) 36
(E) 72
Kudos for correct solution.
Given: \((4^2)^3 \times 2^6=2^y\)
Apply the Power of a Power law to the left side to get: \(4^6 \times 2^6=2^y\)
Rewrite \(4\) as \(2^2\) to get: \((2^2)^6 \times 2^6=2^y\)
Apply the Power of a Power law to the left side to get: \(2^{12} \times 2^6=2^y\)
Apply the Product law to get: \(2^{18} =2^y\)
Since the bases are the same, the exponents must be the same, which means \(18 = y\)
Answer: C
