Respuesta :

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]

tramserran

Answer:   p⁻¹ q⁴ r⁸

Step-by-step explanation:

Use the quotient rule: [tex]\dfrac{x^a}{x^b}=x^{a-b}[/tex]

[tex]\dfrac{p^{-4}q^5r^6}{p^{-3}qr^{-2}}=p^{-4-(-3)}q^{5-(1)}r^{6-(-2)}\\\\.\qquad \qquad =p^{-4+3}q^{5-1}r^{6+2}\\\\.\qquad \qquad =p^{-1}q^{4}r^{8}[/tex]