5a²b⁵c³ . -4a⁷c⁵

Answer 1

To multiply these expressions, we can multiply the coefficients (numbers) separately and then multiply the variables together:

5a²b⁵c³ . -4a⁷c⁵ = (-4)(5)(a²)(a⁷)(b⁵)(c³)(c⁵)

Simplifying the coefficients: (-4)(5) = -20

Simplifying the variables:
a² * a⁷ = a^(2 + 7) = a⁹
b⁵ * c⁵ = b^(5) * c^(3+5) = b⁵c⁸

Putting it all together: -20a⁹b⁵c⁸

Answer 2

2x²y⁴z⁵ . 4x³y⁵z²

Answer 3

To simplify the expression 2x²y⁴z⁵ . 4x³y⁵z², we can multiply the coefficients separately and then multiply the variables together:

2x²y⁴z⁵ . 4x³y⁵z² = (2)(4)(x²)(x³)(y⁴)(y⁵)(z⁵)(z²)

Simplifying the coefficients: (2)(4) = 8

Simplifying the variables:
x² * x³ = x^(2 + 3) = x⁵
y⁴ * y⁵ = y^(4 + 5) = y⁹
z⁵ * z² = z^(5 + 2) = z⁷

Putting it all together: 8x⁵y⁹z⁷

Answer 4

3a³b² (6ab + 7a²b)

Answer 5

To simplify the expression, we need to use the distributive property to multiply each term inside the parentheses by 3a³b²:

3a³b² * 6ab = 18a^(3 + 1)b^(2 + 1) = 18a⁴b³

3a³b² * 7a²b = 21a^(3 + 2)b^(2 + 1) = 21a⁵b³

Combining the two terms:

18a⁴b³ + 21a⁵b³ = 39a⁵b³ + 18a⁴b³ = (39a⁵ + 18a⁴) * b³

The simplified expression is (39a⁵ + 18a⁴) * b³.