Question

((a^7/5)/(a^7/8))^40, при а 2^корень из 6

Answer 1

$( \frac{a^ \frac{7}{5}}{a^ \frac78})^4^0=(a^ \frac{7}{5}^-^ \frac{7}{8})^4^0=(a^ \frac{56}{40}^-^ \frac{35}{40})^4^0=(a^ \frac{21}{40})^4^0=a^\frac{21}{40}^*^4^0=a^2^1=a^2^0*a$$=(2^2^0)^ \sqrt{6}}*2^ \sqrt{6}}=(1024^2)^ \sqrt{6}}*2^ \sqrt{6}}$

Answer 2

$(\frac{a^{\frac{7}{5}}}{a^{\frac{7}{8}}})^{40}=\frac{a^{\frac{7}{5}*40}}{a^{\frac{7}{8}*40}}=\frac{a^{56}}{a^{35}}=a^{56-35}=a^{21};~[a=2^{\sqrt{6}}]~(2^{\sqrt{6}})^{21}=\\(2^{20})^{\sqrt{6}}*2^{\sqrt{6}}=(1024^2)^{\sqrt{6}}*2^{\sqrt{6}}$