Question

Which expression is equivalent to (a^-3 b/a^-5 b3)^-3? Assume a=0, b=0.

Answer 1

`Use:\\\\(a^n)/(a^m)=a^(n-m)\\\\(a^n)^m=a^(nm)\\\\a^(-n)=(1)/(a^n)\\\\(ab)^n=a^nb^n`


`\left((a^(-3)b)/(a^(-5)b^3)\right)^(-3)=\left(a^(-3-(-5))b^(1-3)\right)^(-3)=\left(a^(-3+5)b^(-2)\right)^(-3)=\left(a^2b^(-2)\right)^(-3)\\\\=(a^2)^(-3)(b^(-2))^(-3)=a^(2(-3))b^(-2(-3))=a^(-6)b^6=(b^6)/(a^6)`