Question 214121
Recall that {{{x^(-1)=1/x^1=1/x}}} and {{{x^(-2)=1/x^2}}}. In other words, to rewrite an expression with positive exponents, just flip the base.



So in this case {{{u^(-3)=1/u^3}}}. So {{{2u^(-3)v^2=2(1/u^3)v^2=(2v^2)/u^3}}}



So {{{(2u^(-3)v^2)^(-2)=((2v^2)/u^3)^(-2)}}}




Now flip the fraction to make the outer exponent positive: {{{((2v^2)/u^3)^(-2)=((u^3)/(2v^2))^2}}}



Now simplify to get: {{{((u^3)/(2v^2))^2=(u^6)/(4v^4)}}}


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Answer:


So {{{(2u^(-3)v^2)^(-2)=(u^6)/(4v^4)}}}