Algebra 2 Exponents Cant figure out

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(x^2+4)^1/3(3)-(3x)(1/3)(x^2+4)^-2/3(2x)

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[(x^2+4)^1/3]^2

This is a fraction

Oct 3rd, 2015

Thank you for the opportunity to help you with your question!

(x^2+4)^1/3(3)-(3x)(1/3)(x^2+4)^-2/3(2x)

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[(x^2+4)^1/3]^2

1) Let y = x^2+4

2. Simplify the denominator to y^(2/3)

3) Simplify the numerator to y^1 - xy^(-2/3)(2x), then to y^1 - 2(x^2)y^(-2/3)

4) Now we have y^1 - y^(-2/3) * 2(x^2), all divided by y^(2/3)

5) Multiply numerator and denominator by y^(-2/3), getting

6) [y^(1/3) - y^(-4/3) * 2(x^2)] / y^0 

7) which equals (x^2+4)^(1/3) - (x^2+4)^(-4/3) * 2(x^2)

Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 19th, 2015

the answer key in my book says 

x^2 + 12

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(x^2 +4)^4/3

Sep 19th, 2015

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