Mathematics
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OpenStudy (anonymous):
Simplify. PLEASE HELP. Medal and Fan!
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OpenStudy (anonymous):
\[3\frac{ 1 }{ 2 }\times3\frac{ 1 }{ 2 }\]
OpenStudy (anonymous):
@misty1212 i feel like this is really easy, would it be 6 1/2?
OpenStudy (misty1212):
are these mixed numbers or exponents?
OpenStudy (anonymous):
mixed numbers
OpenStudy (misty1212):
your sure, it is \(3\tfrac{1}{2}\) not \(3^{\frac{1}{2}}\)
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OpenStudy (anonymous):
Wait, youre right. its the second one
OpenStudy (misty1212):
lol how'd i guess?
OpenStudy (anonymous):
lol
OpenStudy (misty1212):
first off if it was mixed numbers it would certainly not be what you wrote
\[\frac{7}{2}\times \frac{7}{2}=\frac{49}{4}=12\tfrac{1}{4}\]
OpenStudy (misty1212):
but since they are exponetns, all you have to do is add them
what is
\[\frac{1}{2}+\frac{1}{2}?\]
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OpenStudy (anonymous):
2/4? or 2/2?
OpenStudy (misty1212):
second one
OpenStudy (anonymous):
1/2
OpenStudy (anonymous):
okay
OpenStudy (misty1212):
oh no dear, how is one half plus one half equal one half?
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OpenStudy (misty1212):
what is one half plus one half?
OpenStudy (anonymous):
i didnt think through that. and 2/2
OpenStudy (anonymous):
1
OpenStudy (misty1212):
whew!
OpenStudy (misty1212):
so \[3^1\] is your answer, better known as \(3\) because we don't really write an exponent if it is one, do we?
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OpenStudy (anonymous):
no
OpenStudy (anonymous):
but we dont times the 3 ?
OpenStudy (misty1212):
\[\color\magenta\heartsuit\]
OpenStudy (misty1212):
times it by what ?
OpenStudy (anonymous):
3*3 is 6? or were just simplifying, not solving, right?
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OpenStudy (misty1212):
this is what you are using
\[b^n\times b^m=b^{n+m}\]
OpenStudy (misty1212):
what you multiply with the same base, you add the exponents
OpenStudy (anonymous):
oh okay so 3 is the answer
OpenStudy (misty1212):
in this case
\[\huge 3^{\frac{1}{2}}\times 3^{\frac{1}{2}}=3^{\frac{1}{2}+\frac{1}{2}}=3^1=3\]
OpenStudy (misty1212):
yes 3 is the answer
btw \(3^{\frac{1}{2}}=\sqrt3\)