Question

algebra ii with statistics 3rd quarter - aaa02
simplifying rational expressions
which expression is equivalent to \\(\frac{-18a^{-2}b^{5}}{-12a^{-4}b^{-6}}\\)? assume \\(a \
eq 0, b \
eq 0\\).
options:
\\(\frac{2a^{2}b^{20}}{3}\\)
\\(\frac{3a^{2}b^{11}}{2}\\)
\\(\frac{2a^{2}b^{11}}{3}\\)
\\(\frac{3a^{2}b^{\text{?}}}{2}\\) (last options exponent is unclear from ocr but follows the pattern)

Explanation:

Step1: Simplify the constant terms

$\frac{-18}{-12} = \frac{3}{2}$

Step2: Simplify the $a$-terms using exponent rules

$a^{-2 - (-4)} = a^{-2 + 4} = a^{2}$

Step3: Simplify the $b$-terms using exponent rules

$b^{5 - (-6)} = b^{5 + 6} = b^{11}$

Step4: Combine all simplified parts

$\frac{3}{2} \times a^{2} \times b^{11} = \frac{3a^{2}b^{11}}{2}$

Answer:

$\boldsymbol{\frac{3a^{2}b^{11}}{2}}$ (matches the second option)