Question

Multiply and simplify by factoring.

^3sqrty^10 3sqrt16y^11=

Answer 1

\[\sqrt[3]{y^{10}} \sqrt[3]{16y^{11}}\]

Answer 2

Is that it ?

Answer 3

yes

Answer 4

Okay. Easiest way is to just write everything out so you can see.

y^10 = (y*y*y) * (y*y*y) * (y*y*y) * y

Answer 5

Any idea why I grouped those 10 that way?

Answer 6

because they cancel out?

Answer 7

Well, since you are taking the cube root, I wanted to group them in groups of 3.

For each group of 3, you can pull that outside the radical.

Answer 8

ok

Answer 9

So that means I can pull out y^3

Answer 10

\[y^3\sqrt[3]{y}\]

Answer 11

16 = (2*2*2) * 2 * 2

Answer 12

and y^11 = (y*y*y) * (y*y*y) * (y*y*y) * y * y

Answer 13

So we can pull out 2y^3

Answer 14

But now we have (y^3)(2y^3) ^3sqrt(y) ^sqrt(y^2)

Combine those last two and we get ^3sqrt(y^3) and that means another y comes out so we are left with

(y^3)(2y^3)(y)

Answer 15

Which is 2y^7

Answer 16

oops

Answer 17

2y^7 ^3sqrt(4)

Answer 18

here is another way for the cognoscenti.
3 (the index) goes in to 10 (the exponent) 3 times with a remainder of 1. so
\[y^3\] comes out and one y stays in

Answer 19

Yeah that is a lot easier. :) Just want to make sure she understands why that is the case.

Answer 20

of course

Answer 21

The other thing too is that at the beginning we should have combined everything to get 16y^21 underneath the radical.

Answer 22

It is then easy to see there are 7 groups of (y*y*y)