The problem asks us to simplify the expression $(9x^3y)(-2x^2yz^5)$.

AlgebraSimplificationPolynomialsExponents
2025/3/10

1. Problem Description

The problem asks us to simplify the expression (9x3y)(2x2yz5)(9x^3y)(-2x^2yz^5).

2. Solution Steps

We need to multiply the two terms together.
First, we multiply the coefficients: 92=189 * -2 = -18.
Next, we multiply the xx terms: x3x2=x3+2=x5x^3 * x^2 = x^{3+2} = x^5.
Then, we multiply the yy terms: yy=y1+1=y2y * y = y^{1+1} = y^2.
Finally, we include the z5z^5 term.
Putting it all together:
xaxb=xa+bx^a * x^b = x^{a+b}
(9x3y)(2x2yz5)=(92)(x3x2)(yy)(z5)=18x5y2z5(9x^3y)(-2x^2yz^5) = (9 * -2)(x^3 * x^2)(y * y)(z^5) = -18x^5y^2z^5.

3. Final Answer

18x5y2z5-18x^5y^2z^5

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