Question

change from radical form to exponential expression in fractional form. No need to evaluate just be put in simplest form

Answer 1

To convert from radical form to exponential in fractional form, we can follow:

`\sqrt[m]{b^n}=b^{(n)/(m)}`

Firstly, notice that 9 is the same as 3 squared:

`\sqrt[4x+2]{9}=\sqrt[4x+2]{3^2}`

Now, we can apply the change:

`\sqrt[4x+2]{3^2}=3^{(2)/(4x+2)}`

Also, notice that we can factor out the 2 on the denominator to cancel with the two on the numerator:

`3^{(2)/(4x+2)}=3^{(2)/(2(2x+1))}=3^{(1)/(2x+1)}`

So, the expression in the simples form and fractional exponent is:

`3^{(1)/(2x+1)}`