No.

The correct equivalent phrases for these expressions should be :


(Half of x)² or 'the square of half of x'


(Double of x)² or 'the square of double of x'
(Twice of x)² or 'the square of twice of x'
(Two times of x)² or 'the square of two times of x'


(A quarter of x)²
or (one-fourth of x)²
or 'the square of a quarter of x'
or 'the square of one-fourth of x'



(Half of x)³ or 'the cube of half of x'


(Double of x)³ or 'the cube of double of x'
(Twice of x)³ or 'the cube of twice of x'
(Two times of x)³ or 'the cube of two times of x'


(A quarter of x)³
or (one-fourth of x)³
or 'the cube of a quarter of x'
or 'the cube of one-fourth of x'

Those phrases you wrote refer to :


'half of x squared' or 'half of x²'
→ ½x²


'Double of x squared' or 'double of x²
→ 2x²


'a quarter of x squared'
or 'a quarter of x²'
or 'one-fourth of x squared'
or 'one-fourth of x²'
→ ¼x²


'half of x cubed' or 'half of x³'
→ ½x³


'Double of x cubed' or 'double of x³
→ 2x³


'a quarter of x cubed'
or 'a quarter of x³'
or 'one-fourth of x cubed'
or 'one-fourth of x³'
→ ¼x³