# Thread: Simplifying using Rational Exponents

1. ## Simplifying using Rational Exponents

Hi everyone!

I have a question on this one problem regarding rational exponents. Here is it:

I got this far:

I'm a little frustrated now because I don't know what the next step is. I would appreciate any help.

Thank you so much, I really appreciate it!

2. ## Re: Simplifying using Rational Exponents

If it were me, I would work first within the parentheses using:

$\sqrt[n]{x^m}=x^{\frac{m}{n}}$

Next, use the rule for exponents:

$a^b\cdot a^c=a^{b+c}$

Then finally use the rule for exponents:

$\left(a^b \right)^c=a^{bc}$

3. ## Re: Simplifying using Rational Exponents

Originally Posted by choti96

I got this far:
Convert these to fractional exponents and combine.
$\sqrt[3]{7} = 7^{\frac{1}{3}} \;\& \,\sqrt[4]{7} = 7^{\frac{1}{4}}$

You simply use the laws of exponents .

4. ## Re: Simplifying using Rational Exponents

Thank you so much, Plato! You are incredible!

5. ## Re: Simplifying using Rational Exponents

Thanks for the help, Mark!