How is -16/(4x+6)^5 and -1/(2(2x+3)^5) equivalent?

Question

I think -1/2(2x+3)^5 is the more simplified version of the two, but I just can't figure out how -16/(4x+6)^5 simplifies to -1/(2(2x+3)^5). please explain

Answer 1

When you factor the denominator you get

(4x+6)^5
= 2^5 (2x + 3)^5
= 32(2x+3)^5

so -16/(4x+6)^5
= -16/(32(2x+3)^5)
= -1/(2(2x+3)^5)

further explanation:

(4x+6)^5
= (4x+6)(4x+6)(4x+6)(4x+6)(4x+6)
= (2)(2x+3)(2)(2x+3)(2)(2x+3)(2)(2x+3)(2)(2x+3)
= 32(2x+3)^5

Answer 2

thanks