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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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