To convert from radical form to exponential in fractional form, we can follow:
[tex]\sqrt[m]{b^n}=b^{\frac{n}{m}}[/tex]
Firstly, notice that 9 is the same as 3 squared:
[tex]\sqrt[4x+2]{9}=\sqrt[4x+2]{3^2}[/tex]
Now, we can apply the change:
[tex]\sqrt[4x+2]{3^2}=3^{\frac{2}{4x+2}}[/tex]
Also, notice that we can factor out the 2 on the denominator to cancel with the two on the numerator:
[tex]3^{\frac{2}{4x+2}}=3^{\frac{2}{2(2x+1)}}=3^{\frac{1}{2x+1}}[/tex]
So, the expression in the simples form and fractional exponent is:
[tex]3^{\frac{1}{2x+1}}[/tex]
