## shelovespiano Group Title Simplify the expression and eliminate any negative exponents, assuming that all letters denote positive numbers. (2x^4 * y^(-4/5))^3(8y^2)^(2/3) I try to post it in equation form too. one year ago one year ago

1. J-Monstur Group Title

Could you draw it out?

2. shelovespiano Group Title

$(2x^4y^\frac{ -4 }{ 5 })^3(8y^2)^\frac{ 2 }{ 3 }$

3. Denebel Group Title

if it was $(a ^{4})^{3}$ What have you learned to do with the exponents?

4. shelovespiano Group Title

Multiply 4 and 3, right?

5. Denebel Group Title

Yes, what if it was $(4a ^{4})^{3}$ ?

6. shelovespiano Group Title

4 to the third times a to the 12

7. Denebel Group Title

Yes, what happens with $(8y ^{2})^{2/3}$ ?

8. shelovespiano Group Title

$8^\frac{ 2 }{ 3 }y ^\frac{ 4 }{ 3 }$

9. Denebel Group Title

Ok, so which part do you have trouble with?

10. shelovespiano Group Title

Well, the answer in the back of the book is 14, and no matter what I do, i can't get 14! I'll take a picture of my work real quick and maybe you can see what I did then?

11. Denebel Group Title

Sure

12. helder_edwin Group Title

$\large (2x^4y^{-4/5})^3(8y^2)^{2/3}=2^3x^{4\times3}y^{-4/5\times3} 8^{2/3}y^{2\times2/3}$

13. helder_edwin Group Title

$\large 8x^{12}y^{-12/5}8^{2/3}y^{4/3}$

14. helder_edwin Group Title

$\large =8^{1+2/3}x^{12}y^{4/3-12/5}=8^{5/3}x^{12}y^{-16/15}$

15. lopus Group Title

|dw:1347151652056:dw|

16. lopus Group Title

$2x^{12}*\frac{ 8 }{ y}$

17. shelovespiano Group Title

Here's what I have... I've just tried a few times and I'm really having difficulty. This is my most recent bit.

18. helder_edwin Group Title

$\large =2^5x^{12}y^{-16/15}$

19. shelovespiano Group Title

According to the back of the book, the answer is $(32x^\frac{ 12 }{ 1 })/(y^ \frac{ 16 }{ 15 })$

20. shelovespiano Group Title

I just don't have an idea of how to get it.

21. helder_edwin Group Title

$\large \frac{32x^{12}}{y^{16/15}}$ 2^5=32

22. lopus Group Title

|dw:1347152276782:dw|

23. Denebel Group Title

You broke down your y's by saying $y ^{4/3}= y \sqrt[3]{y}$ and such...

24. lopus Group Title

$y ^{-1}=\frac{ 1 }{ y }$

25. Denebel Group Title

|dw:1347152573807:dw|

26. shelovespiano Group Title

ok, thanks everyone! i have a better understanding now.