Question

convert from radical form to exponential expression in rational form no need to evaluate just be put in simplest form( i already know how to simplify the multiplication oart i j need help in the division)

Answer 1

In order to convert from radical to exponential form, we can use the property below:

`\sqrt[c]{a^b}=a^{(b)/(c)}`

Then, to find the simplest form, we use this property:

`\begin{gathered} a^b\cdot a^c=a^(b+c) \\ a^b\colon a^c=a^(b-c) \end{gathered}`

So we have:

`\begin{gathered} \sqrt[5]{x^3}=x^{(3)/(5)} \\ \sqrt[]{x^4}=x^{(4)/(2)} \\ \sqrt[]{x^3}=x^{(3)/(2)} \\ \\ \sqrt[5]{x^3}\cdot\sqrt[]{x^4}\colon\sqrt[]{x^3} \\ =x^{(3)/(5)}\cdot x^{(4)/(2)}\colon x^{(3)/(2)} \\ =x^{(3)/(5)+(4)/(2)-(3)/(2)} \\ =x^{(3)/(5)+(1)/(2)} \\ =x^{(6)/(10)+(5)/(10)} \\ =x^{(11)/(10)} \\ =x^1\cdot x^{(1)/(10)} \\ =x\sqrt[10]{x} \end{gathered}`