Can someone tell me if I'm right:
Simplify the given expression to rational exponent form, justify each step by identifying the properties of rational exponents used.
1 over the cube root of the quantity of x to the negative sixth power
= 3squrt x^-6= x^-6/3

Question

Can someone tell me if I'm right:
Simplify the given expression to rational exponent form, justify each step by identifying the properties of rational exponents used. 
1 over the cube root of the quantity of x to the negative sixth power 
= 3squrt x^-6= x^-6/3

anonymous · Answer

$$1/3\sqrt{-6}=3\sqrt{-6}=x^{-6}/3$$

anonymous · Answer

that's suppose to be x^-6 in the squrt

e.mccormick · Answer

$\dfrac{1}{\sqrt[3]{x^{-6}}}$

You can't just take it out from under the 1.

anonymous · Answer

okay...so how so I solve what the question is asking?

e.mccormick · Answer

Deal with the cube first, then it will be in a form where you can use the fact that $\frac{1}{x^{-1}}=x$ to get it out from the bottom of the fraction.

anonymous · Answer

I have to make it a rational exponent though...im kind of confused

e.mccormick · Answer

That is a rational exponent, when you deal with the cube root.  Know what a root is as an exponent?

$\sqrt{x}=x^{\frac{1}{2}}$

So you do the same thing with the cube root, but remembering that there alreadu is the -6 power on x.

anonymous · Answer

$$ x \frac{ 1 }{ -6}?$$

e.mccormick · Answer

Let me show it with some variables.

$\LARGE \sqrt[b]{x^a}=x^{\frac{a}{b}}$

e.mccormick · Answer

See how the b is on the bottom of the fraction in the rational exponent?

anonymous · Answer

$$x \frac{ -6}{ 3 }$$

anonymous · Answer

Like that?

e.mccormick · Answer

Yah.  The - can be out front, but on top is OK too.

e.mccormick · Answer

Now you can use the $\frac{1}{x^{-1}}=x^1$ rule.

anonymous · Answer

okay you lost me

anonymous · Answer

$$x1-\frac{ 6 }{ 3 }$$

e.mccormick · Answer

A negatibve exponent causes something to invert . Some examples right on the top of this: http://www.purplemath.com/modules/simpexpo2.htm

anonymous · Answer

so x will have a negative exponent?

e.mccormick · Answer

No, you want to get rid of the negative part of the exponent. That makes it go from one side of the fraction to the other.  In this case, it gets rid of the 1 over part because there is nothing else to the fraction.

anonymous · Answer

okay so  it will still be:

$$x \frac{ 6 }{ 3}$$
Just know negative sign

e.mccormick · Answer

Correct.  No negative sign and no one over.

And finally, you can simplify the rational exponent.  They work like regular fractions.

e.mccormick · Answer

Then it will be in fully simplified form.

anonymous · Answer

okay...um so do I do 6 divided by 3...sorry i'm really bad at math

e.mccormick · Answer

Yes.  6 divided by 3.

anonymous · Answer

so x2

e.mccormick · Answer

$x^2$  Yep.  That is the final form.

anonymous · Answer

Yeah! Thank you so much for explaining it to me! ^-^

e.mccormick · Answer

When you type up your explanation, use x^(-6/3) because the ( ) make it clear what you mean.

anonymous · Answer

Okay I'll do that Thanks!

e.mccormick · Answer

np.  have fun!