## anonymous one year ago Rewrite in simplest radical form 1/x^-3/6. Please show each step of your process.Thank -you so much

1. anonymous

@peachpi

2. mathstudent55

Is this the problem? |dw:1434407986067:dw|

3. anonymous

yes:)

4. mathstudent55

First, you can reduce 3/6

5. mathstudent55

What is the fraction - 3/6 in simplest terms?

6. anonymous

-1/2

7. mathstudent55

Correct. |dw:1434408138951:dw|

8. mathstudent55

Do you know how to deal with a negative exponent?

9. mathstudent55

Here is the rule for negative exponents: $$\Large a^{-n} = \dfrac{1}{a^n}$$

10. anonymous

1/x^2

11. anonymous

Right?

12. mathstudent55

No. There are two things with the exponent of x we need to deal with. 1. It is a negative exponent. 2. The exponent is a fraction. Let's deal only with the negative sign on the exponent for now.

13. anonymous

Ok:)

14. mathstudent55

Just like the rule above of negative exponents works, this one also works: $$\Large \dfrac{1}{a^{-n}} = a^n$$ A negative exponent in the denominator, is a positive exponent in the numerator.

15. mathstudent55

Notice we have a similar thing to this last rule. We have a fraction with 1 over. Then in the denominator we have x to a negative exponent. It changes into just x to the positive exponent in the numerator, and the denominator disappears.

16. mathstudent55

|dw:1434408609017:dw|

17. mathstudent55

You see how the rule and what we have are similar?

18. anonymous

Yes

19. anonymous

But that wouldn't be our final answer, right?

20. mathstudent55

Correct. We have one more step. We still need to deal with the fractional exponent.

21. mathstudent55

Here is the rule for a fractional exponent with numerator 1: $$\Large a^{\frac{1}{n}} = \sqrt[n]{a}$$

22. mathstudent55

A fractional exponent is a root. The denominator tells you which root it is.

23. mathstudent55

|dw:1434408876045:dw|

24. anonymous

I see. I see

25. mathstudent55

That is the final answer. Here are all the steps in one single drawing: |dw:1434408951600:dw|

26. anonymous

what happened to the 1/2?

27. anonymous

@mathstudent55 sorry :) I'm just curious!

28. anonymous

@mathstudent55 Is there a certain rule for this up above?

29. anonymous

@JasperRayWolf-Alysa88 We used two rules that I wrote above: $$\large a^{-n} = \dfrac{1}{a^n}$$ $$\large a^{\frac{1}{n}} = \sqrt[n] a$$