## xKingx Group Title How do you write this in simplest form? one year ago one year ago

1. xKingx Group Title

2. geoffb Group Title

$\LARGE (b^{x})^{y} = b^{x \times y}$

3. geoffb Group Title

Remember the outside exponent also applies to the 8.

4. mathgirl73 Group Title

everything must be raised to -2/3 power . when raise a product by a power you multiply the exponents

5. xKingx Group Title

@geoffb Can you explain how I'd use that formula with this problem?

6. mathgirl73 Group Title

|dw:1354925885023:dw|

7. mathgirl73 Group Title

|dw:1354925885023:dw|

8. xKingx Group Title

Can you explain what you did in each step so I can make sure I understand it?

9. mathgirl73 Group Title

from the image the exponents looks negative.

10. xKingx Group Title

They are

11. mathgirl73 Group Title

everything has to be raised by the power that is outside the parentheses. so -2/3

12. mathgirl73 Group Title

everything has to be raised by the power that is outside the parentheses. so -2/3

13. mathgirl73 Group Title

8 raised to the -2/3 and a^-3 raised to the -2/3

14. mathgirl73 Group Title

so you have 8^-2/3

15. mathgirl73 Group Title

you have to multiply a^-3 by -2/3

16. mathgirl73 Group Title

so you get in the numerator -3 times -2 = 6 and the denominator 3 times 1=3

17. mathgirl73 Group Title

so you get in the numerator -3 times -2 = 6 and the denominator 3 times 1=3

18. mathgirl73 Group Title

6/3=2 so you have a^2

19. mathgirl73 Group Title

now you will have 8^-2/3 a^2

20. mathgirl73 Group Title

you can't have negative exponents so you drop 8-2/3 down in the denominator and it becomes 8^2/3

21. mathgirl73 Group Title

now you have a^2/8^2/3

22. mathgirl73 Group Title

if you havent learned how to convert fractional exponents to radicals then you can stop there

23. mathgirl73 Group Title

but if not you convert 8 2/3 to a radical

24. mathgirl73 Group Title

|dw:1354927080454:dw|

25. xKingx Group Title

I think I get it lol

26. mathgirl73 Group Title

ok

27. geoffb Group Title

"you can't have negative exponents" Sure you can. The rest of what you said looks good though.

28. mathgirl73 Group Title

you can but 99.9% of the time n Algebra, teachers want the answer using positive exponents.