Áp dụng các tính chất của hàm lũy thừa, ta có:

a) $9^{\frac{2}{5}}.27^{\frac{2}{5}}$

= $(9.27)^{\frac{2}{5}}$

= $(3^{2}.3^{3})^{\frac{2}{5}}$

= $(3^{2+3})^{\frac{2}{5}}$

= $(3^5)^{\frac{2}{5}}$

= $3^{2}=9$

Vậy $9^{\frac{2}{5}}.27^{\frac{2}{5}}=9$

b) $144^{\frac{3}{4}}.9^{\frac{3}{4}}$

= $(\frac{144}{9})^{\frac{3}{4}}$

= $16^{\frac{3}{4}}$

= $(2^{4})^{\frac{3}{4}}$

= $2^{3}=8$

Vậy $144^{\frac{3}{4}}.9^{\frac{3}{4}}=8$

c) $(\frac{1}{16})^{-0,75}+0,25^{\frac{-5}{2}}$

= $16^{0,75}+(\frac{1}{4})^{-\frac{5}{2}}$

= $16^{\frac{3}{4}}+4^{\frac{5}{2}}$

= $(2^{4})^{\frac{3}{4}}+(2^{2})^{\frac{5}{2}}$

= $2^{3}+2^{5}=8+32=40$

Vậy $(\frac{1}{16})^{-0,75}+0,25^{\frac{-5}{2}}=40$

d) $(0,04)^{-1,5}-(0,125)^{-\frac{2}{3}}$

= $(\frac{4}{100})^{-\frac{3}{2}}-(\frac{1}{8})^{-\frac{2}{3}}$

= $(\frac{100}{4})^{\frac{2}{3}}-8^{\frac{2}{3}}$

= $(5^{2})^{\frac{2}{3}}-(2^{3})^{\frac{2}{3}}$

= $5^{3}-2^{2}=125-4=121$

Vậy $(0,04)^{-1,5}-(0,125)^{-\frac{2}{3}}=121$