Question

7.
$(-2y^{4})cdot(xy^{3})^{2}-13x^{2}y^{10}$

Explanation:

Step1: Expand the squared term

Use exponent rule $(ab)^n=a^n b^n$ and $(a^m)^n=a^{mn}$:
$(xy^3)^2 = x^2 (y^3)^2 = x^2 y^{6}$

Step2: Multiply the first two terms

Multiply coefficients and add exponents of like bases:
$(-2y^4) \cdot x^2 y^6 = -2x^2 y^{4+6} = -2x^2 y^{10}$

Step3: Combine like terms

Subtract the two terms with identical variables:
$-2x^2 y^{10} - 13x^2 y^{10} = (-2-13)x^2 y^{10}$

Answer:

$-15x^2 y^{10}$