How do I simplify ((x^-3*y^-1)/(x^2*y*z^2))^-3

Question

How do I simplify the above question

Answer 1

[(x^-3*y^-1)/(x²*y*z²)]^-3

 

Let's do the term inside the brackets [ ] first.  Recall that x^-a = 1/x^a :

 

[...] = 1/(x³*y*x²*y*z²)

 

Combining like terms:

 

[...] = 1/(x⁵*y²*z²) = x^-5*y^-2*z^-2

 

Now let's do [...]^-3.  Multiply each exponent in the [...] by -3:

 

[x^-5*y^-2*z^-2]^-3 = x^(-5)(-3)*y^(-2)(-3)*z^(-2)(-3)

 

= x¹⁵*y⁶*z⁶