Question 132775
Depending on whether you meant: {{{-2^0 + (16^(5/4))/(125^(-2/3))}}} or {{{(-2^0 + (16^(5/4)))/(125^(-2/3))}}} the answer is either 801 or 825.


{{{-2^0 + (16^(5/4))/(125^(-2/3))}}}, but remember that {{{a^(-n)=1/a^n}}}, so:



{{{-2^0 + (16^(5/4))/(125^(-2/3))=-2^0 + (16^(5/4))(125^(2/3))}}}



Now, remember that {{{a^(n/m)=root(m,a^n)=(root(m,a))^n}}}, and {{{a^0=1}}}so:


{{{-2^0 + (16^(5/4))(125^(2/3))=-2^0+(root(4,16))^5(root(3,125))^2=1+(2^5)(5^2)=1+(32)(25)=1+800=801}}}



Or:
{{{(-2^0 + (16^(5/4)))/(125^(-2/3))=(1+32)(25)=33*25=825}}}