Question

Could someone simplify this for a medal and fan please?

Answer 1

(2xy2)2(y2)3.

Answer 2

@jigglypuff314

Answer 3

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

Answer 4

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

Answer 5

\[ (2xy^2)^2(y^2)^3 \]
?

Answer 6

yes that's it

Answer 7

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?

Answer 8

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

Answer 9

six times

Answer 10

@phi where did you go

Answer 11

yes, and the short way to write y*y *y*y*y*y is y^6

so we found \( \left(y^2\right)^3 = y^6\)

Answer 12

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

Answer 13

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) ?

Answer 14

4x xy4 ???

Answer 15

yes, but we can shorten x*x also

Answer 16

4x^2y^4

Answer 17

oh is the answer 4x^2y^10

Answer 18

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

Answer 19

yah I was right thank you

Answer 20

yes, you got the answer before I finished typing.