Question

1. $(3x)(x^{2}y^{3})$
2. $(5a^{3}b)(2ab)$
3. $(18y^{2}x^{3}z)(3x^{8}y^{6}z^{4})$
4. $(2xyz)(-4x^{2}yz)$

Explanation:

Step1: Multiply coefficients, add exponents

$(3x)(x^2y^3) = 3 \cdot x^{1+2} \cdot y^3 = 3x^3y^3$

Step2: Multiply coefficients, add exponents

$(5a^3b)(2ab) = 5 \cdot 2 \cdot a^{3+1} \cdot b^{1+1} = 10a^4b^2$

Step3: Multiply coefficients, add exponents

$(18y^2x^3z)(3x^8y^6z^4) = 18 \cdot 3 \cdot x^{3+8} \cdot y^{2+6} \cdot z^{1+4} = 54x^{11}y^8z^5$

Step4: Multiply coefficients, add exponents

$(2xyz)(-4x^2yz) = 2 \cdot (-4) \cdot x^{1+2} \cdot y^{1+1} \cdot z^{1+1} = -8x^3y^2z^2$

Answer:

1. $3x^3y^3$
2. $10a^4b^2$
3. $54x^{11}y^8z^5$
4. $-8x^3y^2z^2$