Question

Simplify (3xy^2)(4xy)(2xy)^3.
Can you explain how you got your answer

Answer 1

\[(3xy^2)(4xy)(2xy)^3 = (3\times4\times2^3)xy^2 \times xy\times x^3y^3=96x^5y^6\]

Answer 2

where did you get the 3 when you typed x^3 y^3

Answer 3

so you mutiple 3 x 4 x 2^3 you get 60 what is the next step

Answer 4

now do the letter "x"
if we focus only on the x's you have
x*x*x^3
can you simplify that ?

Answer 5

would it be just 3x

Answer 6

no. 3x means x+x+x

we have x*x*x^3
(remember, x^3 is "short-hand" for x*x*x)
so you really have
x*x*x*x*x
people use "short-hand" to write that
do you know how to write it using the "short" way ?

Answer 7

no

Answer 8

in
x*x*x*x*x
how many times is x being multiplied by itself ?

Answer 9

in other words, how many x's do you see ?

Answer 10

4

Answer 11

x*x*x*x*x
that has 5 x's
so the short way to write it is x with a little 5 in the upper right
\[ x^5\]
or write x^5 if we don't use the equation editor

that means so far your answer
is
3*4*2^3 which is 3*4*2*2*2 or 3*4*8 or 12*8 or 96
and x*x*x*x*x or x^5

or
96x^5

now we do the y's

Answer 12

the y's are
y^2 * y * y^3

Answer 13

?

Answer 14

you could do it the long way
what is y^2 written the long way ?
It is y*y

what is y^3 written the long way? do you know ?

Answer 15

y y y

Answer 16

yes, so
y^2 * y * y^3
is also written the long way as
y*y*y* y*y*y

now write that the short-way
can you do that ?

Answer 17

yes it would be y y and just y y y right

Answer 18

the "short-way" means putting a little number in the upper right of y
what number should we use for
y*y*y*y*y*y
?

Answer 19

6

Answer 20

yes, so instead of
y*y*y*y*y*y we write \(y^6\) or y^6
(It's easier to use the short-way, right ?)

Answer 21

yes

Answer 22

so we write
y^2 * y * y^3
as y^6

Answer 23

and the simplified way to write
(3xy^2)(4xy)(2xy)^3
is
96 x^5 y^6

Answer 24

btw, the trickiest part is
(2xy)^3

that is short for writing
(2xy)(2xy)(2xy)
or
2*x*y*2*x*y*2*x*y

when you multiply, you can change the order, so you can write that mess as
2*2*2*x*x*x*y*y*y
or
2^3 x^3 y^3