How to Convert Radical Expressions to Exponential Form

[trentt]

The problem is (\sqrt[4]{6x})^3 And i have to convert it to exponential form, and I forgot how to do this, so i need some help.


Thank you.

 

[Caramon]

$$(\sqrt[4]{6x})^3$$

Step 1:
$$(({6x})^{1/4})^3$$

Step 2:
$$({6x})^{3/4}$$

Technically, you can go farther but this is the simplest and most compact form.

Remember when you are converting the square root into a fraction before you use the fractional exponent rule that, "Roots are located on the bottom," just like how roots of a tree are located at the bottom. That should help you remember!

For example:
$$\sqrt[3]{x^2} = {x}^{2/3}$$

 

[trentt]

$$(\sqrt[4]{6x})^3 = ({6x}^{1/4})^3 = {6x}^{3/4}$$

Technically, you can go farther but... I assume we're going to stop there.

Thanks

 

[trentt]

Actually, if anyone is still looking at this post. Could they also convert
(\sqrt[4]{a^3b^5})^{1/2} To exponential form.

I'm not very smart today.

 

[Caramon]

Thanks

I typed the LaTeX wrong the first time, the last expression should read:
$$({6x})^{3/4}$$

Give that one a shot yourself and tell me where you get stuck, I'll be here reading this so I can help you along. :)
$$(\sqrt[4]{(a^3)(b^5)})^{1/2}$$

Hint: Remember roots are on the bottom, so convert the square root into an exponential expression and then do your exponent rules and simplify!

 

[trentt]

I typed the LaTeX wrong the first time, the last expression should read:
$$({6x})^{3/4}$$

Give that one a shot yourself and tell me where you get stuck, I'll be here reading this so I can help you along. :)
$$(\sqrt[4]{(a^3)(b^5)})^{1/2}$$

Hint: Remember roots are on the bottom, so convert the square root into an exponential expression and then do your exponent rules and simplify!

Thanks, I finished the rest of it.