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if any of that is an "exponent" you should use ^ to show them
\[ (2xy^2)^2(y^2)^3 \] ?
yes that's it
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?
y*y *y*y*y*y is y multiplied by itself how many times?
@phi where did you go
yes, and the short way to write y*y *y*y*y*y is y^6 so we found \( \left(y^2\right)^3 = y^6\)
you can use that same idea for \[ (2xy^2)^2 \] the stuff in parens (no matter how complicated it looks) is multiplied by itself
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) ?
4x xy4 ???
yes, but we can shorten x*x also
oh is the answer 4x^2y^10
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
yah I was right thank you
yes, you got the answer before I finished typing.