Question

1. $2x^{2}y^{4} \cdot 4x^{3}y^{4}$
2. $6x^{4}y^{2} \cdot 2x^{3}y^{2}$
3. $4xy^{2} \cdot 2x^{2}y^{4}$
4. $x^{4}y^{2} \cdot xy^{3}$
5. $ab \cdot 2b^{3} \cdot 2a^{2}$
6. $3u^{3}v^{4} \cdot u^{2}v^{4} \cdot 3uv^{4}$
7. $-9m^{5}n^{5} \cdot -2m^{2}p^{5}$
8. $-9m^{3}p^{6}q^{2} \cdot 3m^{10}q^{8}$
9. $3x^{4}y^{2} \cdot -6y^{8}z^{5}$
10. $2x^{4}z^{5} \cdot 4x^{7}y^{10}z^{10}$

Explanation:

Step1: Multiply coefficients, add exponents (15)

$2 \cdot 4 \cdot x^{2+3} \cdot y^{4+4} = 8x^5y^8$

Step2: Multiply coefficients, add exponents (16)

$6 \cdot 2 \cdot x^{4+3} \cdot y^{2+2} = 12x^7y^4$

Step3: Multiply coefficients, add exponents (17)

$4 \cdot 2 \cdot x^{1+2} \cdot y^{2+4} = 8x^3y^6$

Step4: Multiply coefficients, add exponents (18)

$1 \cdot 1 \cdot x^{4+1} \cdot y^{2+3} = x^5y^5$

Step5: Multiply coefficients, add exponents (19)

$1 \cdot 2 \cdot 2 \cdot a^{1+2} \cdot b^{1+3} = 4a^3b^4$

Step6: Multiply coefficients, add exponents (20)

$3 \cdot 1 \cdot 3 \cdot u^{3+2+1} \cdot v^{4+4+4} = 9u^6v^{12}$

Step7: Multiply coefficients, add exponents (21)

$-9 \cdot (-2) \cdot m^{5+2} \cdot n^5 \cdot p^5 = 18m^7n^5p^5$

Step8: Multiply coefficients, add exponents (22)

$-9 \cdot 3 \cdot m^{3+10} \cdot p^6 \cdot q^{2+8} = -27m^{13}p^6q^{10}$

Step9: Multiply coefficients, add exponents (23)

$3 \cdot (-6) \cdot x^4 \cdot y^{2+8} \cdot z^5 = -18x^4y^{10}z^5$

Step10: Multiply coefficients, add exponents (24)

$2 \cdot 4 \cdot x^{4+7} \cdot y^{10} \cdot z^{5+10} = 8x^{11}y^{10}z^{15}$

Answer:

1. $8x^5y^8$
2. $12x^7y^4$
3. $8x^3y^6$
4. $x^5y^5$
5. $4a^3b^4$
6. $9u^6v^{12}$
7. $18m^7n^5p^5$
8. $-27m^{13}p^6q^{10}$
9. $-18x^4y^{10}z^5$
10. $8x^{11}y^{10}z^{15}$