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just starting gmat prep, silly question : (

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just starting gmat prep, silly question : ( [#permalink] New post 21 Feb 2012, 21:18
Could someone help me to understand why:

5^21*4^11= 2*10^21

thanks :wink:
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Re: just starting gmat prep, silly question : ( [#permalink] New post 21 Feb 2012, 21:36
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alcatraz wrote:
Could someone help me to understand why:

5^21*4^11= 2*10^21

thanks :wink:



Welcome to GMAT Club. Below is a solution for your question:

5^{21}*4^{11}=5^{21}*2^{22}=(5^{21}*2^{21})*2=2*10^{21}.

For more on exponents check Number Theory chapter of Math Book: math-number-theory-88376.html

Questions to practice:
Tough and tricky exponents and roots questions with detailed solution (PS): tough-and-tricky-exponents-and-roots-questions-125956.html
Tough and tricky exponents and roots questions with detailed solution (DS): tough-and-tricky-exponents-and-roots-questions-125967.html

Hope it helps.

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Re: just starting gmat prep, silly question : ( [#permalink] New post 22 Feb 2012, 08:47
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alcatraz wrote:
5^21*4^11= 2*10^21


On the right hand side:
- 10 is 5 * 2
- so, 10^{21} is (5 * 2)^{21} which is the same as 5^{21} * 2^{21}


On the left hand side:
4^{11} is (2 * 2)^{11},
....which is the same as 2^{11} * 2^{11}
....which is 2^{22},
....which is 2^1 * 2^{21}

So, now the left hand side can be re-written as:
5^{21} * (2^1 * 2^{21})
Rearranging:
2^1 * (5^{21} * 2^{21})
or:
2 * (10^{21}).
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Re: just starting gmat prep, silly question : ( [#permalink] New post 22 Feb 2012, 08:49
and, oh btw: no question's really silly. not, imho. :-D
Re: just starting gmat prep, silly question : (   [#permalink] 22 Feb 2012, 08:49
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