[tex]a) (2^2*4^2*8^2*1^{16})^2=(2^2*2^{2*2}*2^{3*2}*1)^2=(2^2*2^4*2^6)^2=(2^{12})^2=2^{24}\\\\b)5^3*15^2*25^3*(\frac{1}{125})^3 =5^3*3*5^2*5^{2*3}*\frac{1}{5^{3*3}}=\\ \\= 5^3*3*5^2*5^6*\frac{1}{5^{9}} = 3*5^{11}*\frac{1}{5^{9}} =3*5^2 = 3*25 = 75\\\\c)(\frac{-1}{3^5})^2 = \frac{1}{3^{10}}\\[/tex]