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Pre-Calculus

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

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

  • Pre-Calculus - ,

    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

  • Pre-Calculus - ,

    thanks

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