To simplify the given equation we need to review the rules of power:
[tex](1) \ a^{m} * a^{n} = a^{m+n} \\ (2) \ \frac{a^{m}}{a^{n}} = a^{m-n} \\ (3) \ (a^{m} )^{n} = a^{mn} \\
(4) a^{-m} = \frac{1}{ a^{m} } [/tex]
[tex](5) \ (ab)^{m} = a^{m} * b^{m} [/tex]
The given equation is
[tex]( \frac{2ab}{ a^{-5} b^{2} } )^{3} [/tex]
= [tex]2^{3} * ( \frac{a}{ a^{-5} } )^3 * ( \frac{b}{ b^{2}} )^3 [/tex]
= [tex]8 * ( a^{1-(-5)} )^3 * ( b^{1-2} )^3[/tex]
= [tex]8 * ( a^{6} )^3 * ( b^{-1} )^3[/tex]
= [tex]8 * a^{18} * b^{-3} [/tex]
= [tex] \frac{8a^{18}}{ b^{3} } [/tex]
