how do I rewrite expressions using rational exponent notation? And can you give me examples please?

You mean scientific notation?

Scientific notation - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Scientific_notation)

It consists of converting a large number into a number with only one digit before the decimal place, it uses the fact that

10^x is the same as 1 followed by x 0s. As I'm sure you are familiar, dividing or multiplying by a power of 10 "just moves the decimal place."

This enables us to express large or small numbers in more concise terms.

for example 0.0000000000000000000000023 is annoying to write out, so we look at where we want the decimal point to be (between the 2 and 3) and count the number of places back to the decimal point (24), so in this case we can rewrite it in a more concise manner:

0.0000000000000000000000023 = 2.3*10^{-24} = 2.3E-24

This last statement 2.3E-24 is "exponential notation".

We can get back to the original number like so:

2.3E-24 = 2.3*10^{-24} = 2.3*0.0000000000000000000000001 = 0.0000000000000000000000023

Capuchin, From a Google search I don't think that's what it means.
I looked on Google and I think this is what the OP means:

\left(\sqrt[y] {x^n}\right)^z=x^{\frac {nz} y}

See, we converted the equation to a form which has a rational exponent.

I wasn't familiar with the term either.

As the OP requested, here are some examples:

\sqrt[3] 11 = 11^{\frac 1 3} \\
\sqrt[5] {3^8} = 3^{\frac 8 5} \\
{\sqrt[7] 4}^8 = 4^{\frac 8 7} \\
{\sqrt[13] {9^3}}^4=9^{\frac {3*4} {13}}=9^{\frac {12} {13}}


Put the root number on the bottom of the fraction, put the exponents on the top of the fraction.