Question 180130
{{{-((8a^3)/(27))^(-4/3)}}} Start with the given expression



{{{-(27/(8a^3))^(4/3)}}} Flip the fraction to make the exponent positive



Note: {{{(a/b)^(-2)=(b/a)^2}}}




{{{-(root(3,27/(8a^3)))^4}}} Convert to radical notation



{{{-(root(3,27)/root(3,8a^3))^4}}} Break up the root.



{{{-(3/root(3,8a^3))^4}}} Take the cube root of 27 to get 3



{{{-(3/(2a))^4}}} Take the cube root of {{{8a^3}}} to get {{{2a}}}. Note: {{{(2a)^3=2^3*a^3=8a^3}}}



{{{-3^4/(2a)^4}}} Distribute the outer exponent



{{{-81/(2a)^4}}} Raise 3 to the 4th power to get 81



{{{-81/(16a^4)}}} Raise {{{2a}}} to the 4th power to get {{{16a^4}}}



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Answer:



So {{{-((8a^3)/(27))^(-4/3)=-81/(16a^4)}}} where {{{a>0}}}