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D01-05

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Bunuel
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D01-05 [#permalink] New post   16 Sep 2014, 00:11
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Which of the following expressions has the greatest value?

A. \(999^{12}\)
B. \(10^{30}\)
C. \(777^{10}\)
D. \((-20)^{24}\)
E. \((\sqrt{15})^{40}\)
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Bunuel
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Re D01-05 [#permalink] New post   16 Sep 2014, 00:11
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Official Solution:

Which of the following expressions has the greatest value?

A. \(999^{12}\)
B. \(10^{30}\)
C. \(777^{10}\)
D. \((-20)^{24}\)
E. \((\sqrt{15})^{40}\)


Let's compare the options:

Option C (\(777^{10}\)) is less than Option B (\(10^{30}=1000^{10}\)), because \(777 < 1000\).

Option E (\((\sqrt{15})^{40} =15^{20}\)) is less than Option D (\(20^{24}\)), as both the base and the exponent in E are smaller than those in D.

Option B (\(10^{30}=(10^5)^6\)) is less than Option D (\(20^{24}=(20^4)^6=(16*10^4)^6\)), because \(10^5 < 16*10^4\).

Lastly, Option D (\(400^{12}\)) is less than Option A (\(999^{12}\)), because \(400 < 999\).


Answer: A
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Re: D01-05 [#permalink] New post   18 May 2016, 09:17
Bunuel wrote:

B. \(10^{30} = 1000^{10}\)


I promise I'm typically quite good with the exponent rules but for some reason I can't wrap my head around this one; can someone please break the rule out on this one as to why it's to the 10th?
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Re: D01-05 [#permalink] New post   18 May 2016, 10:30
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redfield wrote:
Bunuel wrote:

B. \(10^{30} = 1000^{10}\)


I promise I'm typically quite good with the exponent rules but for some reason I can't wrap my head around this one; can someone please break the rule out on this one as to why it's to the 10th?


\((a^m)^n=a^{mn}\)

\(10^{30} = 10^{3*10}=(10^3)^{10}=1000^{10}\).

Theory on Exponents: math-number-theory-88376.html
Tips on Exponents: exponents-and-roots-on-the-gmat-tips-and-hints-174993.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html
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Re: D01-05 [#permalink] New post   19 Apr 2023, 13:48
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re D01-05 [#permalink] New post   12 Aug 2023, 09:43
I think this is a high-quality question and I agree with explanation.
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D01-05 [#permalink] New post   01 Dec 2023, 15:33
I don't get why 10^30 is not the same as 1,000^28? You have 30 tens, you use one (10*10=100) 100^29, then you use another (100*10= 1,000) 1,000^28
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Re: D01-05 [#permalink] New post   02 Dec 2023, 01:41
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hbelden97 wrote:
I don't get why 10^30 is not the same as 1,000^28? You have 30 tens, you use one (10*10=100) 100^29, then you use another (100*10= 1,000) 1,000^28


That's not how exponentiation works.

\(10^{30} = 10^{2*15} = (10^2)^{15}=100^{15}\), which does not equal to \(100^{29}\).

\(10^{30} = 10^{3*10} = (10^3)^{10}=1,000^{10}\), which does not equal to \(1,000^{28}\).

8. Exponents and Roots of Numbers




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Re D01-05 [#permalink] New post   21 Mar 2024, 06:02
I think this is a high-quality question and I agree with explanation.
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