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m >1

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Carcass
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m >1 [#permalink] New post   05 May 2022, 06:26
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\(m >1\)


Quantity A
Quantity B
\(\sqrt{m^{12}} \)
\( (m^2)^5\)



A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

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B
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GreenlightTestPrep
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Re: m >1 [#permalink] New post   05 May 2022, 07:20
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Carcass wrote:
\(m >1\)


Quantity A
Quantity B
\(\sqrt{m^{12}} \)
\( (m^2)^5\)




Key concept: If \(x > 0\), then \(\sqrt{x} = x^{\frac{1}{2}}\)

So, we can rewrite Quantity A as follows:
QUANTITY A: \((m^{12})^{\frac{1}{2}}\)
QUANTITY B: \( (m^2)^5\)

Apply the power of a power law to both quantities to get:
QUANTITY A: \(m^{6}\)
QUANTITY B: \(m^{10}\)

Since \(m > 1\), we can be certain that Quantity B is greater.
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Re: m >1 [#permalink] New post   05 May 2022, 11:38
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Option A = sq m^12 = m ^ 12/2 = m^6

Option B = (m^2)^5 = m ^ 2*5 = m^ 10

Since m>1, option B > A, hence the correct ans
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Re: m >1 [#permalink]
05 May 2022, 11:38
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