Question

Please someone answer this please

Answer 1

Option C:

$\frac{3 a^{2} b^{11}}{2 }$ is equivalent to the given expression.

Solution:

Given expression:

$\frac{-18 a^{-2} b^{5}}{-12 a^{-4} b^{-6}}$

To find which expression is equivalent to the given expression.

$\frac{-18 a^{-2} b^{5}}{-12 a^{-4} b^{-6}}$

Using exponent rule: $\frac{1}{a^m}=a^{-m}, \ \ \frac{1}{a^{-m}}=a^{m}$

    $=\frac{-18 a^{-2} b^{5}a^{4} b^{6}}{-12 }$

    $=\frac{-18 a^{-2} a^{4} b^{5} b^{6}}{-12 }$

Using exponent rule: ${a^m}\cdot{a^n}=a^{m+n}$

    $=\frac{-18 a^{(-2+4)} b^{(5+6)}}{-12 }$

   $=\frac{-18 a^{2} b^{11}}{-12 }$

Divide both numerator and denominator by the common factor –6.

   $=\frac{3 a^{2} b^{11}}{2 }$

$\frac{-18 a^{-2} b^{5}}{-12 a^{-4} b^{-6}}=\frac{3 a^{2} b^{11}}{2 }$

Therefore, $\frac{3 a^{2} b^{11}}{2 }$ is equivalent to the given expression.

Hence Option C is the correct answer.