we are given
[tex] \frac{\sqrt[3]{7}\sqrt{7}}{\sqrt[6]{7^5}} [/tex]
we can write it in terms of exponents
[tex] \frac{7^{\frac{1}{3}}*7^{\frac{1}{2}}}{7^{\frac{5}{6}}} [/tex]
Firstly , we will simplify numerator
[tex] \frac{7^{\frac{1}{3}+\frac{1}{2}}}{7^{\frac{5}{6}}} [/tex]
now, we can add exponents
[tex] \frac{7^{\frac{5}{6}}}{7^{\frac{5}{6}}} [/tex]
we can cancel it
and we get
[tex] =1 [/tex]............Answer
