C) \( \left(5 a b^{2}\right)(-12 a b)\left(-3 y^{4} b^{2}\right)= \) D) \( \left(7 x^{2}\right)\left(-9 x^{3} y^{2}\right)\left(3 x^{2} y^{3}\right)= \) e) \( \left(-3 x^{2} y^{3}\right)\left(-5 x^{2} y^{4}\right)\left(10 x^{3} y^{2}\right)= \) F) \( \left(5 a^{2} b^{3}\right)\left(12 a^{2} b^{2}\right)(3 b)= \) G) \( \left(-6 a^{2}\right)\left(a^{2}\right)(-4 a)= \) H) \( (4 x y)\left(2 x^{2} y+7 x^{3} y^{4}+6\right)= \) I) \( (4 x)\left(10 g+7 x^{3}+4 x^{5}\right)= \)

Let's simplify each expression step by step. ### C) \( \left(5 a b^{2}\right)(-12 a b)\left(-3 y^{4} b^{2}\right) \) 1. Multiply the coefficients: \( 5 \times -12 \times -3 = 180 \) 2. Combine the \( a \) terms: \( a^1 \times a^1 = a^{1+1} = a^2 \) 3. Combine the \( b \) terms: \( b^2 \times b^1 \times b^2 = b^{2+1+2} = b^5 \) 4. The \( y \) term remains: \( y^4 \) Putting it all together: \[ C = 180 a^2 b^5 y^4 \] ### D) \( \left(7 x^{2}\right)\left(-9 x^{3} y^{2}\right)\left(3 x^{2} y^{3}\right) \) 1. Multiply the coefficients: \( 7 \times -9 \times 3 = -189 \) 2. Combine the \( x \) terms: \( x^2 \times x^3 \times x^2 = x^{2+3+2} = x^7 \) 3. Combine the \( y \) terms: \( y^0 \times y^2 \times y^3 = y^{0+2+3} = y^5 \) Putting it all together: \[ D = -189 x^7 y^5 \] ### E) \( \left(-3 x^{2} y^{3}\right)\left(-5 x^{2} y^{4}\right)\left(10 x^{3} y^{2}\right) \) 1. Multiply the coefficients: \( -3 \times -5 \times 10 = 150 \) 2. Combine the \( x \) terms: \( x^2 \times x^2 \times x^3 = x^{2+2+3} = x^7 \) 3. Combine the \( y \) terms: \( y^3 \times y^4 \times y^2 = y^{3+4+2} = y^9 \) Putting it all together: \[ E = 150 x^7 y^9 \] ### F) \( \left(5 a^{2} b^{3}\right)\left(12 a^{2} b^{2}\right)(3 b) \) 1. Multiply the coefficients: \( 5 \times 12 \times 3 = 180 \) 2. Combine the \( a \) terms: \( a^2 \times a^2 = a^{2+2} = a^4 \) 3. Combine the \( b \) terms: \( b^3 \times b^2 \times b^1 = b^{3+2+1} = b^6 \) Putting it all together: \[ F = 180 a^4 b^6 \] ### G) \( \left(-6 a^{2}\right)\left(a^{2}\right)(-4 a) \) 1. Multiply the coefficients: \( -6 \times 1 \times -4 = 24 \) 2. Combine the \( a \) terms: \( a^2 \times a^2 \times a^1 = a^{2+2+1} = a^5 \) Putting it all together: \[ G = 24 a^5 \] ### H) \( (4 x y)\left(2 x^{2} y+7 x^{3} y^{4}+6\right) \) Distributing \( 4xy \): 1. \( 4xy \cdot 2x^2y = 8x^{3}y^{2} \) 2. \( 4xy \cdot 7x^3y^4 = 28x^{4}y^{5} \) 3. \( 4xy \cdot 6 = 24xy \) Putting it all together: \[ H = 8x^3y^2 + 28x^4y^5 + 24xy \] ### I) \( (4 x)\left(10 g+7 x^{3}+4 x^{5}\right) \) Distributing \( 4x \): 1. \( 4x \cdot 10g = 40xg \) 2. \( 4x \cdot 7x^3 = 28x^4 \) 3. \( 4x \cdot 4x^5 = 16x