Question

Simplify (3xy^2)(4xy)(2xy)^3.

24x3y2
24x5y6
96x5y6
96x3y3

Answer 1

Let's start by simplifying the inside of the parentheses. The first two can be left as they are, but (2xy)^3 can be simplified.
2^3 is 8, so we can rewrite (2xy)^3 as 8x^3y^3
Now we have (3xy^2)(4xy)(8x^3y^3)
Next, we can move forward by grouping the same variables and grouping the numbers together the same way.
(3*4*8)(x*x*x^3)(y^2*y*y^3)
After that, it's just multiplication to get the final answer.
3*4*8 is 96. And remember that when you multiply variables with exponents, you *add* the exponents together to get the final result.
So, x*x*x^3 is the same as x^(1+1+3), which simplifies to x^5, for example.

Answer 2

I'm gonna just reword that in LaTeX because that was kind of crowded. Credit still goes to you, of course.

\(\color{teal}{\text{Originally Posted by}}\) @SmokeyBrown
Let's start by simplifying the inside of the parentheses. The first two can be left as they are, but \({2xy}^3\) can be simplified.

\(2^3\) is 8, so we can rewrite \({2xy}^3\) as \({8x}^3y^3\)
Now we have\[{(3xy}^2)(4xy)({8x}^3{y}^3)\]

Next, we can move forward by grouping the same variables and grouping the numbers together the same way.\[(3\cdot4\cdot8)(x\cdot x\cdot x^3)(y^2\cdot y\cdot y^3)\]
After that, it's just multiplication to get the final answer.

\(3\cdot4\cdot8\) is 96. And remember that when you multiply variables with exponents, you add the exponents together to get the final result.
So, \(x\cdot x\cdot x^3\) is the same as \(x^{1+1+3}\), which simplifies to \(x^5\), for example.
\(\color{teal}{\text{End of Quote}}\)