exponent help please: solve 64x^6 = 27

[Guitarman]

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]

Simplify the sixth root of 27/64.

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

Eliz.

 

[pka]

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

 

[Guitarman]

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]

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.