Question

Simplify the following expressions. Then determine the value of the polynomial when a=−1 and when b=3.

a) (3ab³)³
b) (−2a²⋅b)⋅(−4ab)²

Options:
a. a=−81,b=729a=−81,b=729
b. a=−243,b=729a=−243,b=729
c. a=−81,b=81a=−81,b=81
d. a=−27,b=729a=−27,b=729

Answer 1

To simplify the expressions, we apply the rules of exponents. The value of the polynomial when a = -1 and b = 3 is -531441 for the first expression and -864 for the second expression. The correct option is d. a = -27, b = 729.

Step-by-step explanation:

To simplify the given expressions, we need to apply the rules of exponents. Let's simplify each expression step by step:

a) (3ab³)³ = 3³ * a³ * (b³)³ = 27a³b⁹

b) (−2a²⋅b)⋅(−4ab)² = (-2 * a² * b) * (-4 * a * b)² = (-2 * -4²)a³b³ = 32a³b³

To determine the value of each polynomial when a = -1 and b = 3:

a) Substitute a = -1 and b = 3 into 27a³b⁹: 27(-1)³(3)⁹ = 27(-1)(19683) = -531441

b) Substitute a = -1 and b = 3 into 32a³b³: 32(-1)³(3)³ = 32(-1)(27) = -864

Therefore, the correct option is d. a = -27, b = 729.