## xKingx 2 years ago How do you write this in simplest form?

1. xKingx

2. geoffb

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

3. geoffb

Remember the outside exponent also applies to the 8.

4. mathgirl73

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

5. xKingx

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

6. mathgirl73

|dw:1354925885023:dw|

7. mathgirl73

|dw:1354925885023:dw|

8. xKingx

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

9. mathgirl73

from the image the exponents looks negative.

10. xKingx

They are

11. mathgirl73

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

12. mathgirl73

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

13. mathgirl73

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

14. mathgirl73

so you have 8^-2/3

15. mathgirl73

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

16. mathgirl73

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

17. mathgirl73

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

18. mathgirl73

6/3=2 so you have a^2

19. mathgirl73

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

20. mathgirl73

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

21. mathgirl73

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

22. mathgirl73

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

23. mathgirl73

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

24. mathgirl73

|dw:1354927080454:dw|

25. xKingx

I think I get it lol

26. mathgirl73

ok

27. geoffb

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

28. mathgirl73

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