Answer:
[tex]\frac{p^{-4}q^{5}r^{6}}{p^{-3}qr^{-2}}=p^{-1}q^{4}r^{8}[/tex]
Step-by-step explanation:
In division of powers with the same base, we must subtract the exponent of the denominator from the exponent of the numerator:
[tex]\frac{a^{m}}{a^{n}}=a^{m-n}[/tex]
Then applying this to the problem:
[tex]\frac{p^{-4}q^{5}r^{6}}{p^{-3}qr^{-2}}=p^{-4-(-3)}q^{5-1}r^{6-(-2)}[/tex]
Eliminating the parentheses:
[tex]\frac{p^{-4}q^{5}r^{6}}{p^{-3}qr^{-2}}=p^{-4+3}q^{5-1}r^{6+2}\\ \frac{p^{-4}q^{5}r^{6}}{p^{-3}qr^{-2}}=p^{-1}q^{4}r^{8}[/tex]
