Question

which represents this expression in its simplest form?
$\frac{18(x^{-3})^{2}}{3(x^{-3})^{-4}}$
○ $\frac{15}{x^6}$
○ $15x^{18}$
○ $\frac{6}{x^6}$
○ $\frac{6}{x^{18}}$

Explanation:

Step1: Simplify numerator coefficient

$\frac{18}{3} = 6$

Step2: Simplify exponent of $x^{-3}$

$(x^{-3})^{2 - (-4)} = (x^{-3})^{6}$

Step3: Calculate final exponent

$x^{-3 \times 6} = x^{-18} = \frac{1}{x^{18}}$

Step4: Combine coefficient and variable

$6 \times \frac{1}{x^{18}} = \frac{6}{x^{18}}$

Answer:

$\boldsymbol{\frac{6}{x^{18}}}$ (corresponding to the last option)