Question

Using the Rules of Exponents. Please show me how to simplify each expression.

27 -2/3
____

27 -1/3

Answer 1

I would reorder the entire fraction first, to make working with the fractions easier

-2/3+27
________

-1/3+27

Then we should multiply each side of the fraction by the denominator's conjugate.

-2/3+27 (1/3+27)
________________

-1/3+27 (1/3+27)

-2/3+27 (1/3+27) =6478/9

-1/3+27 (1/3+27) =6560/9

You now have a fraction divided by another fraction. you can reorder them by using the reciprocal of the denominator fraction, which allows you to now multiply the two fractions.

6478
____

9
_________

6560
____

9

turns into...

6478 9
____ x _____

9 6560

From here, you multiply across.

You now have:
58302 79
______ Which simplifies into: __

59040 80

79/80 is your final simplified answer. Sorry this is so long, but this is a tough problem.

Answer 2

Well, the spacing was kinda off on that as usual, but hopefully you get the idea.