Question

question 15(multiple choice worth 1 points) (06.03 lc) simplify $\frac{-6a^{3}b^{-1}}{36ab^{2}}$. -6a²b³; -$\frac{a^{2}}{6b^{3}}$; -$\frac{a^{2}b^{3}}{6}$; -$\frac{6a^{2}}{b^{3}}$

Explanation:

Step1: Simplify coefficient

$\frac{-6}{36}=-\frac{1}{6}$

Step2: Apply exponent - rule for $a$ terms

$\frac{a^{3}}{a}=a^{3 - 1}=a^{2}$ (using $\frac{x^{m}}{x^{n}}=x^{m - n}$)

Step3: Apply exponent - rule for $b$ terms

$\frac{b^{-1}}{b^{2}}=b^{-1-2}=b^{-3}=\frac{1}{b^{3}}$ (using $\frac{x^{m}}{x^{n}}=x^{m - n}$)

Step4: Combine results

$-\frac{1}{6}\times a^{2}\times\frac{1}{b^{3}}=-\frac{a^{2}}{6b^{3}}$

Answer:

$-\frac{a^{2}}{6b^{3}}$ (corresponding to the second option in the multiple - choice list, assuming the second option is meant to be $-\frac{a^{2}}{6b^{3}}$ as the formatting in the image is a bit unclear)