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# just starting gmat prep, silly question : (

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Intern
Joined: 06 Feb 2012
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just starting gmat prep, silly question : ( [#permalink]

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21 Feb 2012, 21:18
Could someone help me to understand why:

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

thanks
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Re: just starting gmat prep, silly question : ( [#permalink]

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21 Feb 2012, 21:36
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Expert's post
alcatraz wrote:
Could someone help me to understand why:

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

thanks

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]

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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]

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22 Feb 2012, 08:49
and, oh btw: no question's really silly. not, imho.
Re: just starting gmat prep, silly question : (   [#permalink] 22 Feb 2012, 08:49
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