[ASK] Exponents and Roots

Apr 2018
159
37
Sukoharjo
The result of \(\displaystyle \frac{7x-\frac92\sqrt[6]{y^5}}{\left(x^{\frac56}-6y^{-\frac13}\right)x^{-2}}\) for x = 4 and y = 27 is ....
a. \(\displaystyle \left(1+2\sqrt2\right)9\sqrt2\)
b. \(\displaystyle \left(1+2\sqrt2\right)9\sqrt3\)
c. \(\displaystyle \left(1+2\sqrt2\right)18\sqrt3\)
d. \(\displaystyle \left(1+2\sqrt2\right)27\sqrt2\)
e. \(\displaystyle \left(1+2\sqrt2\right)27\sqrt3\)

I got stuck at \(\displaystyle \frac{56-3^2\left(3^{\frac52}\right)}{2^-{\frac43}-2^{-2}}\) and don't know how to continue to reach one of the options. By the way, don't you think that 7 is suspicious?
 
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