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5^9 or 25^4

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Carcass
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5^9 or 25^4 [#permalink] New post   09 May 2022, 02:00
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Quantity A
Quantity B
\( 5^9\)
\(25^4\)



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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A
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GreenlightTestPrep
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Re: 5^9 or 25^4 [#permalink] New post   09 May 2022, 05:58
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Carcass wrote:
Quantity A
Quantity B
\( 5^9\)
\(25^4\)




Given:
QUANTITY A: \( 5^9\)
QUANTITY B: \(25^4\)

Strategy: It's much easier to compare powers when they have the same base.
So let's rewrite \(25\) as \(5^2\) and go from there:

QUANTITY A: \( 5^9\)
QUANTITY B: \((5^2)^4\)

Apply the power of a power law to Quantity B to get:
QUANTITY A: \( 5^9\)
QUANTITY B: \(5^8\)

At this point, it's clear that Quantity A is greater.

Answer: A
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AjinkyaGupta88
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Re: 5^9 or 25^4 [#permalink] New post   10 May 2022, 02:52
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thumb rule to compare indices is by bringing them to its prime factors.

B can be further reduced to (5^2)^4 which is equal to 5^8

A is given as 5^9.

Hence, A is greater and so A is the answer.
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Re: 5^9 or 25^4 [#permalink]
10 May 2022, 02:52
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