Question

$(ab)^{3} cdot 2a^{4}b^{-4}$
a) $4b^{4}a^{10}$
b) $\frac{1}{b^{6}a^{4}}$
c) $\frac{2a^{7}}{b}$
d) $b^{7}$
〇 a
〇 b
〇 c
〇 d

Explanation:

Step1: Expand the power term

$(ab)^3 = a^3b^3$

Step2: Rewrite the original expression

$a^3b^3 \cdot 2a^4b^{-4}$

Step3: Combine like terms for $a$

$a^{3+4} = a^7$

Step4: Combine like terms for $b$

$b^{3+(-4)} = b^{-1} = \frac{1}{b}$

Step5: Multiply with the constant

$2 \cdot a^7 \cdot \frac{1}{b} = \frac{2a^7}{b}$

Answer:

C) $\frac{2a^7}{b}$