exponent help please: solve 64x^6 = 27

Guitarman

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Aug 22, 2006
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Solve 64x^6 = 27

I've gotten to:

. . .(x^6)^1/6=27/64^1/6

But I have no clue where to go from there. I'm looking for the real solutions for this problem. Is there a solution? I just need to know where to go next. Thank you.
 

stapel

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Feb 4, 2004
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Simplify the sixth root of 27/64.

Note: There should probably be a "plus-minus" sign on the (27/64)^(1/6).

Eliz.
 

pka

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Jan 29, 2005
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What you need to know is that:\(\displaystyle 3^3 = 27\quad \& \quad 4^3 = 64\)
 

Guitarman

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Aug 22, 2006
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stapel said:
Simplify the sixth root of 27/64.
I don't want to sound stupid, but how do I simplify the sixth root of 27/64? Which buttons do I press on my TI-86?
 

pka

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Guitarman said:
I don't want to sound stupid, but how do I simplify the sixth root of 27/64? Which buttons do I press on my TI-86?
JUST FORGET YOUR TI-86.
It is of no use to you here.
This is all about fundamentals!

\(\displaystyle \sqrt[6]{{\frac{{27}}{{64}}}} = \sqrt[6]{{\frac{{3^3 }}{{4^3 }}}} = \left( {\frac{{3^3 }}{{4^3 }}} \right)^{\frac{1}{6}} = \frac{{3^{\frac{1}{2}} }}{{4^{\frac{1}{2}} }} = \sqrt {\frac{3}{4}}\)

The TI-86 cannot help you understand that. You must understand the basics.
Otherwise the calculator is useless.
 
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