Mathematics
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OpenStudy (anonymous):
Which is equal to (√2)^5?
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OpenStudy (anonymous):
Options:
\[2\frac{ 1 }{ 10 }\]
\[2\frac{ 2 }{ 5 }\]
\[2\frac{ 5 }{ 2 }\]
\[2^{10}\]
OpenStudy (vishweshshrimali5):
Ok
OpenStudy (anonymous):
I think it's D, \[2^{10}\]
OpenStudy (vishweshshrimali5):
Have you given it some try ?
OpenStudy (anonymous):
Because 5*2=10 so 2 is to the 10th power
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OpenStudy (vishweshshrimali5):
No, actually it is 1/2 * 5 = 5/2
OpenStudy (anonymous):
I suck at algebra (can you tell?) I really wish I got to take 2 years of geometry instead of this lol
OpenStudy (vishweshshrimali5):
Its okay
OpenStudy (anonymous):
So it'd be \[2\frac{ 5 }{ 2 }\]
OpenStudy (vishweshshrimali5):
See:
by law of exponents we have:
|dw:1402811295716:dw|
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OpenStudy (vishweshshrimali5):
Now, here, a = 2 and m = 1/2 (because square root means power 1/2 ) and n is ?
OpenStudy (vishweshshrimali5):
Can you guess ?
OpenStudy (anonymous):
1?
OpenStudy (vishweshshrimali5):
Well I would be back in 1 hour.
OpenStudy (vishweshshrimali5):
No, n is 5 here
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OpenStudy (tkhunny):
\(\sqrt{2}^{5} = \sqrt{2}^2\cdot\sqrt{2}^2\cdot \sqrt{2}\)
OpenStudy (anonymous):
Thank you @vishweshshrimali5 and @tkhunny for answering!
OpenStudy (tkhunny):
Are you sure we're not supposed to be talking about \(\left(2^{2}\right)^{5}\)?