Question

1. $-4x^{2}(-4x)^{2}=$
2. $(xy^{3})^{2}(x^{2}y)^{3}=$

Explanation:

Step1: Expand $(-4x)^2$

$(-4x)^2 = (-4)^2 \cdot x^2 = 16x^2$

Step2: Multiply with $-4x^2$

$-4x^2 \cdot 16x^2 = (-4 \times 16) \cdot (x^2 \cdot x^2) = -64x^{2+2} = -64x^4$

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Step1: Expand $(xy^3)^2$

$(xy^3)^2 = x^2 \cdot (y^3)^2 = x^2y^{6}$

Step2: Expand $(x^2y)^3$

$(x^2y)^3 = (x^2)^3 \cdot y^3 = x^{6}y^{3}$

Step3: Multiply the two results

$x^2y^6 \cdot x^6y^3 = (x^2 \cdot x^6) \cdot (y^6 \cdot y^3) = x^{2+6}y^{6+3} = x^8y^9$

Answer:

1. $-64x^4$
2. $x^8y^9$