Question

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

Answer 1

Given the expression:

$(\frac{16x^{1/6}y^{-2}}{x^{-1/6}y^6})^{3/2}$

We use the following property of exponents:

$\frac{z^a}{z^b}=z^{a-b}$

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:

$4^{2\cdot3/2}x^{1/3\cdot3/2}y^{-8\cdot3/2}=4^3x^{1/2}y^{-12}=\frac{64x^{1/2}}{y^{12}}$

Answer: Option D