Question

NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at Math.

Which expression is equivalent to (1/√y)^-1/5?

A: 5√y^2

B: 1/√y^5

C: 10√y

D: 1/10√y​

Answer 1

`=\sqrt[10]{y}`

So option c is the correct answer

Explanation:

`\left((1)/(√(y))\right)^{(-1)/(5)}\\\mathrm{Apply\:exponent\:rule}:\quad \left((a)/(b)\right)^c=(a^c)/(b^c)\\\left((1)/(√(y))\right)^{(-1)/(5)}=\frac{1^{(-1)/(5)}}{\left(√(y)\right)^{(-1)/(5)}}\\=\frac{1^{(-1)/(5)}}{\left(√(y)\right)^{(-1)/(5)}}\\\mathrm{Apply\:rule}\:1^a=1\\1^{(-1)/(5)}=1\\=\frac{1}{\left(√(y)\right)^{(-1)/(5)}}\\\mathrm{Apply\:the\:fraction\:rule}:\quad (-a)/(b)=-(a)/(b)`

`=\frac{1}{\left(√(y)\right)^{-(1)/(5)}}\\\left(√(y)\right)^{-(1)/(5)}=\frac{1}{\sqrt[10]{y}}\\=\frac{1}{\frac{1}{\sqrt[10]{y}}}\\\mathrm{Apply\:the\:fraction\:rule}:\quad (1)/((b)/(c))=(c)/(b)\\=\frac{\sqrt[10]{y}}{1}\\\mathrm{Apply\:rule}\:(a)/(1)=a\\=\sqrt[10]{y}`