Mathematics
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OpenStudy (anonymous):
ok, i need to simplyfy this and show all working: 3^3 / sqrt3^5
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OpenStudy (anonymous):
\[3^{3}\div \sqrt{3^{5}}\]
OpenStudy (nowhereman):
You should use \[\sqrt{x} = x^{\frac{1}{2}}\]
OpenStudy (anonymous):
how
OpenStudy (nowhereman):
use power rules, and \[\frac{x}{y} = x\cdot y^{-1}\]
OpenStudy (nowhereman):
You do have the same bases there, so all you need no know then is what \[x^a \cdot x^b\] is
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OpenStudy (anonymous):
oh, so it will be like \[3^{3-(1/5)}\] right?
OpenStudy (nowhereman):
nearly, but: \[\left( x^a \right) ^b = x^{a\cdot b} \]
OpenStudy (anonymous):
\[\sqrt{3^{5}} = 3^{1/5} . so you get 3^{3}/ \]
OpenStudy (anonymous):
you get 3^3 / 3^1/5
OpenStudy (anonymous):
sqrt3
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OpenStudy (anonymous):
hence that will be \[3^{3-1/5}\]
OpenStudy (nowhereman):
that is exactly the mistake! \[ \sqrt{3^5} = \left( 3^5 \right)^{\frac{1}{2}}\]
OpenStudy (anonymous):
oh no i think i get it wrong. that should be 3^5/2
OpenStudy (anonymous):
hence, its \[3^{3-}\]
OpenStudy (anonymous):
My answer is true SQRT(3)
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OpenStudy (anonymous):
its 3^3-5/2 = 3^1/2
OpenStudy (nowhereman):
And just for completeness, \[x^{\frac{1}{5}} = \sqrt[5]{x} \]
OpenStudy (anonymous):
the answer is \[\sqrt{3}\] right?
OpenStudy (anonymous):
duc, how do you get sqrt3?
OpenStudy (anonymous):
I know the answere, but I dont know how to get to the answer
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OpenStudy (anonymous):
\[3^{3-5/2}\]
OpenStudy (anonymous):
ok, guys, i appreciate you helping me, i just became your fan
OpenStudy (anonymous):
First , You 3^5=3*3^4, so SQRT(3^5)=SQRT(3)*3^2,===>(3^3)/(SQRT(3)*3^2)=3/SQRT(3)=SQRT(3)
It may be TRUE
OpenStudy (anonymous):
ok, thankyou
OpenStudy (anonymous):
No problem() good luck