## anonymous one year ago Could someone simplify this for a medal and fan please?

1. anonymous

(2xy2)2(y2)3.

2. anonymous

@jigglypuff314

3. phi

if any of that is an "exponent" you should use ^ to show them

4. anonymous

(2xy^2)^2(y^2)^3.

5. phi

$(2xy^2)^2(y^2)^3$ ?

6. anonymous

yes that's it

7. phi

there are rules , but if you remember that the little exponent means "multiply by itself" that many times, you can figure it out. for example if you have (stuff)^3 that means stuff*stuff*stuff in other words, if we look just at the (y^2)^3 that means y^2 * y^2 * y^2 or , if we write y^2 as y*y, it means y*y *y*y*y*y you can use the exponent idea to write that a short way, right? what is y*y *y*y*y*y using exponents?

8. phi

y*y *y*y*y*y is y multiplied by itself how many times?

9. anonymous

six times

10. anonymous

@phi where did you go

11. phi

yes, and the short way to write y*y *y*y*y*y is y^6 so we found $$\left(y^2\right)^3 = y^6$$

12. phi

you can use that same idea for $(2xy^2)^2$ the stuff in parens (no matter how complicated it looks) is multiplied by itself

13. phi

in other words $(2xy^2)^2 = (2xy^2)(2xy^2)$ when you multiply , you can change the order $2\cdot 2 \cdot x \cdot x \cdot y^2 \cdot y^2$ can you simplify that (using exponents to "shorten" some of it) ?

14. anonymous

4x xy4 ???

15. phi

yes, but we can shorten x*x also

16. anonymous

4x^2y^4

17. anonymous

18. phi

and we also have from (y^2)^3 a y^6 which we should multiply by 4x^2y^4 * y^6 you could expand out y^4 times y^6 but common sense should tell you you end up with y times itself 10 times

19. anonymous

yah I was right thank you

20. phi

yes, you got the answer before I finished typing.