Question

I need help on this question I’m trying to understand it more better answer 14

Answer 1

Given the expression:

`((16x^(1/6)y^(-2))/(x^(-1/6)y^6))^(3/2)`

We use the following property of exponents:

`(z^a)/(z^b)=z^(a-b)`

Then:

`(16x^(1/6+1/6)y^(-2-6))^(3/2)=(4^2x^(1/3)y^(-8))^(3/2)`

Now, we use the following property of exponents:

`(z^a)^b=z^(a\cdot b)`

Finally:

`4^(2\cdot3/2)x^(1/3\cdot3/2)y^(-8\cdot3/2)=4^3x^(1/2)y^(-12)=(64x^(1/2))/(y^(12))`

Answer: Option D