Question

Aplicando as propriedades da potenciação, transforme a expressão em uma única potência:

$\frac{(a^{3}b)^{3} . (ab^{2})^{-1} }{a^{4}b^{-3} }$

Answer 1

$\dfrac{(a^3 b)^3\cdot (ab^2)^{-1}}{a^4 b^{-3}}\\\\\\ =\dfrac{(a^{3\,\cdot\,3}\cdot b^3)\cdot (a^{-1}\cdot b^{2\,\cdot\,(-1)})}{a^4\cdot b^{-3}}\\\\\\ =\dfrac{(a^{9}\cdot b^3)\cdot (a^{-1}\cdot b^{-2})}{a^4\cdot b^{-3}}\\\\\\ =\dfrac{a^{9-1}\cdot b^{3-2}}{a^4\cdot b^{-3}}\\\\\\ =\dfrac{a^8\cdot b^1}{a^4\cdot b^{-3}}\\\\\\ =\dfrac{a^8}{a^4}\cdot \dfrac{b^1}{b^{-3}}$

$=a^{8-4}\cdot b^{1-(-3)}\\\\ =\boxed{\begin{array}{c}a^{4} b^{4} \end{array}}$


Bons estudos! :-)