which expression is equivalent to $\frac{-18a^{-2}b^{5}}{-12a^{-4}b^{-6}}$? assume $a\neq0,b\neq0$.\n$\frac{2…

which expression is equivalent to $\frac{-18a^{-2}b^{5}}{-12a^{-4}b^{-6}}$? assume $a\neq0,b\neq0$.\n$\frac{2a^{2}b^{11}}{3}$\n$\frac{2a^{2}b^{30}}{3}$\n$\frac{3a^{2}b^{11}}{2}$\n$\frac{3a^{2}b^{30}}{2}$

which expression is equivalent to $\frac{-18a^{-2}b^{5}}{-12a^{-4}b^{-6}}$? assume $a\neq0,b\neq0$.\n$\frac{2a^{2}b^{11}}{3}$\n$\frac{2a^{2}b^{30}}{3}$\n$\frac{3a^{2}b^{11}}{2}$\n$\frac{3a^{2}b^{30}}{2}$

Answer

Explanation:

Step1: Simplify the coefficient

Divide -18 by -12: $\frac{-18}{-12}=\frac{3}{2}$.

Step2: Use exponent - subtraction rule for $a$ terms

For $a$ terms, $a^{-2}\div a^{-4}=a^{-2-(-4)} = a^{-2 + 4}=a^{2}$ according to the rule $x^{m}\div x^{n}=x^{m - n}$.

Step3: Use exponent - subtraction rule for $b$ terms

For $b$ terms, $b^{5}\div b^{-6}=b^{5-(-6)}=b^{5 + 6}=b^{11}$ according to the rule $x^{m}\div x^{n}=x^{m - n}$.

Step4: Combine the results

The equivalent expression is $\frac{3a^{2}b^{11}}{2}$.

Answer:

C. $\frac{3a^{2}b^{11}}{2}$