Question

7.
8.
9.
10.
11.
12.
13.
14.
15.

Explanation:

Problem 7:

Step1: Multiply coefficients

$5 \times (-3) = -15$

Step2: Multiply variable terms

$x^2 \times x^4 = x^{2+4} = x^6$

Step3: Combine results

$-15x^6$

Problem 8:

Step1: Expand the squared term

$(-2x^2y)^2 = (-2)^2(x^2)^2y^2 = 4x^4y^2$

Step2: Multiply by the second term

$4x^4y^2 \times (-3xy^3) = 4\times(-3)x^{4+1}y^{2+3}$

Step3: Simplify the expression

$-12x^5y^5$

Problem 9:

Step1: Multiply coefficients

$2 \times 5 = 10$

Step2: Multiply variable terms

$a^4b^2 \times a^2b^3 = a^{4+2}b^{2+3} = a^6b^5$

Step3: Combine results

$10a^6b^5$

Problem 10:

Step1: Apply power of a power rule

$(-4y^4)^2 = (-4)^2(y^4)^2$

Step2: Simplify each part

$16y^{4\times2} = 16y^8$

Problem 11:

Step1: Expand first power term

$(a^2bc^3)^4 = a^{2\times4}b^4c^{3\times4} = a^8b^4c^{12}$

Step2: Expand second power term

$(b^2c)^3 = b^{2\times3}c^3 = b^6c^3$

Step3: Multiply the two expressions

$a^8b^4c^{12} \times b^6c^3 = a^8b^{4+6}c^{12+3}$

Step4: Simplify exponents

$a^8b^{10}c^{15}$

Problem 12:

Step1: Apply power of a power rule

$(6cd^3)^3 = 6^3c^3d^{3\times3}$

Step2: Calculate coefficient and exponents

$216c^3d^9$

Problem 13:

Step1: Expand the power term

$(4a)^3 = 4^3a^3 = 64a^3$

Step2: Multiply by $a^4$

$64a^3 \times a^4 = 64a^{3+4}$

Step3: Simplify exponent

$64a^7$

Problem 14:

Step1: Expand first power term

$(3xy)^2 = 3^2x^2y^2 = 9x^2y^2$

Step2: Expand second power term

$(-4x^3y^2)^3 = (-4)^3x^{3\times3}y^{2\times3} = -64x^9y^6$

Step3: Multiply the two expressions

$9x^2y^2 \times (-64x^9y^6) = 9\times(-64)x^{2+9}y^{2+6}$

Step4: Simplify coefficient and exponents

$-576x^{11}y^8$

Problem 15:

Step1: Apply power of a power rule

$(4a^3b^2c^2)^4 = 4^4a^{3\times4}b^{2\times4}c^{2\times4}$

Step2: Calculate coefficient and exponents

$256a^{12}b^8c^8$

Answer:

1. $\boldsymbol{-15x^6}$
2. $\boldsymbol{-12x^5y^5}$
3. $\boldsymbol{10a^6b^5}$
4. $\boldsymbol{16y^8}$
5. $\boldsymbol{a^8b^{10}c^{15}}$
6. $\boldsymbol{216c^3d^9}$
7. $\boldsymbol{64a^7}$
8. $\boldsymbol{-576x^{11}y^8}$
9. $\boldsymbol{256a^{12}b^8c^8}$