Simplify and write with positive exponet

Question

(4x^-1)^-1

Work:
(1/4x)^-1
(1/(1/4x))(4x/4x)= 1

(X^3+3x^2+3x+1)^-2/3

Work
1/(X^3+3x^2+3x+1)^2/3
1/(X^2+52/25x^4/3+52/25x+1)

I'm confused on whether these are right or not can someone check my work or explain to me why they're wrong if they are?

Answer 1

how about this way:
using (ab)^n = (a^n)(b^n)

(4x^-1)^-1
= (4^-1)(x^-1)^-1
= (1/4)(x^1)
= (1/4)x
or
= x/4

#2

(x^3+3x^2+3x+1)^(-2/3)
= 1/(x^3+3x^2+3x+1)^(2/3)

notice I assumed your exponent was -2/3,
the way you typed it, the exponent would have been -2 , with 3 a divisor
( (x^3+3x^2+3x+1)^-2 )/3

your last line of 1/(X^2+52/25x^4/3+52/25x+1)
makes absolutely no sense to me