Tính:

a) $9^{\frac{2}{5}}.{27}^{\frac{2}{5}}$;

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

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

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

Hướng dẫn giải:

a) $9^{\frac{2}{5}}.{27}^{\frac{2}{5}}={(9.27)}^{\frac{2}{5}}={\left(3^5\right)}^{\frac{2}{5}}=3^2=9$

b) $\frac{{144}^{{\displaystyle \frac{3}{4}}}}{9^{{\displaystyle \frac{3}{4}}}}={\left(\frac{144}{9}\right)}^{\frac{3}{4}}={16}^{\frac{3}{4}}={\left(2^4\right)}^{\frac{3}{4}}=2^3=8$

c) ${\left(\frac{1}{16}\right)}^{-0,75}+0,{25}^{-\frac{5}{2}}={\left(2^{-4}\right)}^{-0.75}+{\left(2^{-2}\right)}^{-\frac{5}{2}}=2^3+2^5=8+32=40$

d) ${(0,04)}^{-1,5}-{(0,125)}^{-\frac{2}{3}}={\left(\frac{1}{25}\right)}^{-\frac{3}{2}}-{\left(\frac{1}{8}\right)}^{-\frac{2}{3}}={\left(5^{-2}\right)}^{-\frac{3}{2}}-{\left(2^{-3}\right)}^{-\frac{2}{3}}=5^3-2^2=121$