Question

(\frac{1}{4}(4a^{3}b)^{2}(5a^{-7}b^{2}))

Explanation:

Step1: Multiply coefficients first

$\frac{1}{4} \times 4 \times 5 = 5$

Step2: Combine $a$ terms via exponent rule

$a^{3} \times a^{-7} = a^{3 + (-7)} = a^{-4}$

Step3: Combine $b$ terms via exponent rule

$b^{1} \times b^{2} = b^{1+2} = b^{3}$

Step4: Combine all simplified parts

$5 \times a^{-4} \times b^{3} = \frac{5b^3}{a^4}$

Answer:

$\frac{5b^3}{a^4}$