we are given
[tex] \frac{\sqrt[3]{7}\sqrt{7}}{\sqrt[6]{7^5}} [/tex]
we can rewrite it in exponential form
[tex] \frac{7^{\frac{1}{3}}*7^{\frac{1}{2}}}{7^{\frac{5}{6}}} [/tex]
Since, numerator terms are multiplied
so, we can add exponents
we get
[tex] =\frac{7^{\frac{1}{3}+\frac{1}{2}}}{7^{\frac{5}{6}}} [/tex]
[tex] =\frac{7^{\frac{5}{6}}}{7^{\frac{5}{6}}} [/tex]
we can see that numerator and denominator are same
so, they will get cancelled
and we get
[tex] =1 [/tex]..............Answer
