Question

express the following fraction in simplest form, only using positive exponents.
$\frac{-6q^{-1}}{-2(q^{3})^{4}}$

Explanation:

Step1: Simplify coefficient & negative sign

$\frac{-6}{-2} = 3$

Step2: Simplify $(q^3)^4$ via exponent rule

$(q^3)^4 = q^{3\times4}=q^{12}$

Step3: Rewrite $q^{-1}$ with positive exponent

$q^{-1} = \frac{1}{q}$

Step4: Combine terms & simplify exponents

$\frac{3}{q^{12} \times q} = \frac{3}{q^{13}}$

Answer:

$\frac{3}{q^{13}}$