## anonymous one year ago Rewrite in simplest radical form 1 x −3 6 . Show each step of your process.

1. anonymous

|dw:1437531698638:dw|

2. anonymous

@ospreytriple

3. anonymous

First, I would reduce the exponent of x. What do you get?

4. anonymous

-1/2

5. anonymous

Right on. So now you have$\frac{ 1 }{ x ^{-\frac{ 1 }{ 2 }} }$Is that right?

6. anonymous

yes

7. anonymous

OK, I hope you will agree that$\frac{ 1 }{ x ^{-\frac{ 1 }{ 2 }} } = \left( \frac{ 1 }{ x } \right)^{-\frac{ 1 }{ 2 }}$You OK with that?

8. anonymous

yes

9. anonymous

Perfect. Now, to invert the base, you must change the sign of the exponent. For example,$3^{-2} = \left( \frac{ 1 }{ 3 } \right)^{2}$ or$\left( \frac{ 1 }{ 4 } \right)^{5} = 4^{-5}$Gwt the idea? You need to do the same thing with$\left( \frac{ 1 }{ x } \right)^{-\frac{ 1 }{ 2 }}$What do you get?

10. anonymous

x to the pwer of 2?

11. anonymous

Don't invert the exponent, just change its sign. Invert the BASE, and change the sign on the EXPONENT. Try again?

12. anonymous

x to the power of 1/2?

13. anonymous

Perfect. Now write it in radical form.

14. anonymous

In general, fractional exponents are written in radical form like this:$x ^{\frac{ a }{ b }} = \sqrt[b]{x ^{a}}$

15. anonymous

$\sqrt{x}$

16. anonymous

Well done!

17. anonymous

thank you again!