(-3xy^2)^2(-2x^5y^3)^3
(-3xy^2)^2(-2x^5y^3)^3
= (9x^2 y^4)(-8 x^15 y^9)
=-72 x^17 y^13
To simplify the expression (-3xy^2)^2(-2x^5y^3)^3, we need to apply the rules of exponents.
First, let's simplify the exponent of (-3xy^2)^2:
(-3xy^2)^2 = (-3)^2 * (x)^2 * (y^2)^2
= 9 * x^2 * y^(2*2)
= 9x^2y^4
Next, let's simplify the exponent of (-2x^5y^3)^3:
(-2x^5y^3)^3 = (-2)^3 * (x^5)^3 * (y^3)^3
= -8 * x^(5*3) * y^(3*3)
= -8x^15y^9
Now, we can multiply the simplified expressions:
(9x^2y^4) * (-8x^15y^9)
To multiply the terms with the same base (x and y), we add their exponents. So:
9 * -8 = -72
x^2 * x^15 = x^(2 + 15) = x^17
y^4 * y^9 = y^(4 + 9) = y^13
Combining all the terms, the final simplified expression is:
-72x^17y^13