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Ok well do they want you to re-write it with fractional exponents? or ?

It says re-write with rational exponents

Okay, well sqrt6 is like a power of 1/6. Let's see if we can apply that..

\[\sqrt[a]{x}=x^\frac{1}{a}\]

\[\sqrt[a]{b^kc^n}=(b^k c^n)^\frac{1}{a}=b^\frac{k}{a}c^\frac{n}{a}\]

The index of your radical what you will divide your powers by.

There's an 'is' missing from that sentence.

So in this case we have:
\[\sqrt[6]{xy^5z}\]
We can rewrite it as:
\[\large (xy^5z)^{\frac{1}{6}}\]

And the recall that when you raise a power to a power you multiply the exponents.

Raise a product to a power that is.

You just divide each of the exponents by the index of the radical.

What is the exponent on the x ?

1?

Let's start at the beginning.
Do you know how to write
\[\sqrt{x}= x^{?}\]

Correct. So now divide that 1 by 6 and the new exponent on the x will be 1/6

thank you.

Now do the same thing for the y. The exponent on the y is 5, so 5 divided by 6 is 5/6

Then again for the z and your result is:
\[\large x^{\frac{1}{6}}y^{\frac{5}{6}}z^{\frac{1}{6}}\]

which doesn't seem 'simpler' at all. But that's sometimes how that goes.