# exponent help please: solve 64x^6 = 27

#### Guitarman

##### New member
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

##### Super Moderator
Staff member
Simplify the sixth root of 27/64.

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

Eliz.

#### pka

##### Elite Member
What you need to know is that:$$\displaystyle 3^3 = 27\quad \& \quad 4^3 = 64$$

#### Guitarman

##### New member
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

##### Elite Member
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?
It is of no use to you here.

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

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