Question

How do you simplify `(\frac { 4^ { - 1} } { y ^ { 6} x} ) ^ { - 4}`?

Answer 1

`[(4^(-1))/(y^6x)]^-4`

First, distribute the exponent (-4) to each term within the fraction:
`=(4^(-1))^(-4)/(y^6x)^(-4)`
`=(4^4)/(y^(-24)x^(-4))`

We can rewrite any negative exponents on the denominator by moving the terms to the numerator and making the exponents positive:
`=(4^4)y^24x^4`

Now simplify terms:
`=256x^4y^24`