tiffanyanncoope
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Multiply or divide as indicated. Leave your answer with no factors in the denominator.

p^-4 q^5 r^6 / p^-3 qr^-2



Answer :

semsee45

Answer:

[tex]\dfrac{q^{4} r^8}{p}[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{p^{-4}q^5r^6}{p^{-3}qr^{-2}}[/tex]

Separate the variables:

[tex]\implies\dfrac{p^{-4}}{p^{-3}} \times \dfrac{q^5}{q} \times \dfrac{r^6}{r^{-2}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies p^{(-4-(-3)} \times q^{(5-1)} \times r^{(6-(-2)}[/tex]

[tex]\implies p^{(-4+3)} \times q^{(5-1)} \times r^{(6+2)}[/tex]

[tex]\implies p^{-1} \times q^{4} \times r^8[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies \dfrac{1}{p} \times q^{4} \times r^8[/tex]

Simplify:

[tex]\implies \dfrac{q^{4} \times r^8}{p}[/tex]

[tex]\implies \dfrac{q^{4} r^8}{p}[/tex]

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