Answer:
[tex]-\frac{3p^8}{4q^3}[/tex]
Step-by-step explanation:
[tex]\frac{15p^{-4}q^{-6}}{-20p^{-12}q^{-3}}[/tex] can be broken down into three fractions, coefficients, powers of p, powers of q.
[tex]-\frac{15}{20}\cdot\frac{p^{-4}}{p^{-12}}\cdot\frac{q^{-6}}{q^{-3}}[/tex]
Simplify the first fraction, then simplify the others by subtracting numerator exponents minus denominator exponents.
[tex]-\frac{3}{4} p^{-4-(-12)} q^{-6-(-3)} =-\frac{3}{4} p^8 q^{-3} = \alpha -\frac{3p^8}{4q^3}[/tex]
