The problem requires us to multiply monomials in several expressions. The given expressions are: 1. $(-3b^4)(10b^2)$

1. Problem Description

The problem requires us to multiply monomials in several expressions. The given expressions are:

1. $(-3b^4)(10b^2)$

2. $(-31v^1)(-2v^4)$

3. $(4m^8)(-15m^3)$

4. $(x^3)(7x^2)(2x^{10})$

5. $(7n^2)(3n^7)(-4n^7)$

6. $(2x^3)(c^2)(-10c^3)(x^2)$

2. Solution Steps

Let's solve each expression separately.

1. $(-3b^4)(10b^2) = (-3 \times 10)(b^4 \times b^2) = -30b^{4+2} = -30b^6$

2. $(-31v^1)(-2v^4) = (-31 \times -2)(v^1 \times v^4) = 62v^{1+4} = 62v^5$

3. $(4m^8)(-15m^3) = (4 \times -15)(m^8 \times m^3) = -60m^{8+3} = -60m^{11}$

4. $(x^3)(7x^2)(2x^{10}) = (1 \times 7 \times 2)(x^3 \times x^2 \times x^{10}) = 14x^{3+2+10} = 14x^{15}$

5. $(7n^2)(3n^7)(-4n^7) = (7 \times 3 \times -4)(n^2 \times n^7 \times n^7) = -84n^{2+7+7} = -84n^{16}$

6. $(2x^3)(c^2)(-10c^3)(x^2) = (2 \times -10)(x^3 \times x^2)(c^2 \times c^3) = -20x^{3+2}c^{2+3} = -20x^5c^5$

3. Final Answer

1. $-30b^6$

2. $62v^5$

3. $-60m^{11}$

4. $14x^{15}$

5. $-84n^{16}$

6. $-20x^5c^5$