For this case we have the following expression:
[tex](\frac {-27x ^ 0 * y ^ {- 2}} {54x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =[/tex]
By definition we have to:
[tex]a^0 = 1[/tex]
So:
[tex](\frac {-27y ^ {- 2}} {54x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =[/tex]
Simplifying:
[tex](\frac {-y ^ {- 2}} {2x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =[/tex]
By definition of power properties we have to:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
So, rewriting the expression we have:
[tex](-1)^{-2}\frac{-y^{-2*-2}}{2^{-2}*x^{-5*-2}*y^{-4*-2}}=\\\frac{1}{(-1)^2}*\frac{-y^{4}}{2^{-2}x^{10}*y^{8}}=[/tex]
SImplifying:
[tex]+1*\frac{y^{4-8}}{2^{-2}x^{10}}=\\\frac{y^{-4}}{2^{-2}x^{10}}=\\\frac{2^2}{x^{10}y^{4}}[/tex]
Answer:
[tex]\frac{4}{x^{10}y^{4}}[/tex]
