SOLUTION: (-4xyz)(-2x^2.y^3.z^4) I know the answer is 8x^3.y^4.z^5 but i need steps to understand and the formula to use in other questions.

To get the hang of it, follow these steps.  Then later you can shorten the
process.  But at first do it step by step.

(-4xyz)(-2x2∙y3∙z4)

Everything here is multiplication, so put multiplication dots between
every pair of factors, letters and numbers and also between the parentheses:

(-4∙x∙y∙z)∙(-2∙x2∙y3∙z4)

Multiply the numbers -4 times the -2 and get +8 or just 8
Just write the 8 first and eliminate the -4 and the -2

8(x∙y∙z)∙(x2∙y3∙z4)

Write the letters over and over as many times as the exponent says:
That is, instead of x2 write x two times: x∙x
Instead of y3 write y three times: y∙y∙y
Instead of z4 write z four times: z∙z∙z∙z

8∙(x∙y∙z)∙(x∙x∙y∙y∙y∙z∙z∙z∙z)

Since everything is multiplied, you don't need the parentheses,
so eliminate them

8∙x∙y∙z∙x∙x∙y∙y∙y∙z∙z∙z∙z

Arrange the letters in alphabetical order:

8∙x∙x∙x∙y∙y∙y∙y∙z∙z∙z∙z∙z

Count the number of x's. There are 3 of them, so write x3 instead of x∙x∙x

Count the number of y's. There are 4 of them, so write y4 instead of y∙y∙y∙y

Count the number of z's. There are 5 of them, so write z5 instead of z∙z∙z∙z∙z

8∙x3∙y4∙z5

Finally you can erase the multiplication dots if you like.

8x3y4z5

Now you can gradually over time, start shortening the process by skipping steps, but be careful!

Edwin