Respuesta :
Answer:
[tex]\dfrac{7p^{15}}{3q^{12}}[/tex]
Step-by-step explanation:
We want to determine which expression is equivalent to:
[tex]\dfrac{28p^{9}q^{-5} }{12p^{-6}q^7} , p\neq0, q\neq 0[/tex]
To simplify, we first let us separate the fraction in terms of the terms.
[tex]\dfrac{28p^{9}q^{-5} }{12p^{-6}q^7} =\dfrac{28 }{12} X\dfrac{p^{9} }{p^{-6}} X\dfrac{q^{-5}}{q^7}[/tex]
Next, we apply the division law of indices: [tex]\dfrac{a^x}{a^y}=a^{x-y}[/tex]
[tex]\dfrac{28 }{12} Xp^{9-(-6)}Xq^{-5-7}\\=\dfrac{7}{3}Xp^{15}Xq^{-12}\\$Using negative index law of indices: a^{-n}=\dfrac{1}{a^n} \\=\dfrac{7p^{15}}{3q^{12}}[/tex]
Therefore:
[tex]\dfrac{28p^{9}q^{-5} }{12p^{-6}q^7}=\dfrac{7p^{15}}{3q^{12}}[/tex]
The expression that is equivalent to (28p^(9)•q^(-5))/(12p^(6)•q^(7)) is; 7p³/q^(12)
We want to find the fraction that is equivalent to;
(28p^(9)•q^(-5))/(12p^(6)•q^(7))
Applying laws of exponents we know that;
x⁴/x³ = x^(4 - 3)
Thus in our question;
(28p^(9)•q^(-5))/(12p^(6)•q^(7)) gives;
(28/12) × p^(9 - 6) × q^(-5 - 7)
>> (7/3) × p³ × q^(-12)
>> 7p³/q^(12)
Read more about rules of exponents at; https://brainly.com/question/11388301
