Respuesta :
Answer:
Option D.
Step-by-step explanation:
The given expression is
[tex]\dfrac{(5ab)^3}{30a^{-6}b^{-7}}[/tex]
We need to find the expression, which is equivalent to the given expression.
The given expression can be rewritten as
[tex]\dfrac{5^3a^3b^3}{30a^{-6}b^{-7}}[/tex] [tex][\because (ab)^m=a^mb^m][/tex]
[tex]\dfrac{125}{30}\times \dfrac{a^3}{a^{-6}}\times \dfrac{b^3}{b^{-7}}[/tex]
[tex]\dfrac{25}{6}\times a^{3-(-6)}\times b^{3-(-7)}[/tex] [tex][\because \dfrac{a^m}{a^n}=a^{m-n}][/tex]
[tex]\dfrac{25}{6}\times a^{3+6}\times b^{3+7}[/tex]
[tex]\dfrac{25a^9b^{10}}{6}[/tex]
Therefore, the correct option is D.
