## anonymous 4 years ago How do you write this in simplest form?

1. anonymous

2. anonymous

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

3. anonymous

Remember the outside exponent also applies to the 8.

4. anonymous

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

5. anonymous

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

6. anonymous

|dw:1354925885023:dw|

7. anonymous

|dw:1354925885023:dw|

8. anonymous

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

9. anonymous

from the image the exponents looks negative.

10. anonymous

They are

11. anonymous

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

12. anonymous

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

13. anonymous

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

14. anonymous

so you have 8^-2/3

15. anonymous

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

16. anonymous

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

17. anonymous

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

18. anonymous

6/3=2 so you have a^2

19. anonymous

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

20. anonymous

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

21. anonymous

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

22. anonymous

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

23. anonymous

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

24. anonymous

|dw:1354927080454:dw|

25. anonymous

I think I get it lol

26. anonymous

ok

27. anonymous

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

28. anonymous

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