(Math)Simplifying using the laws of exponents

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I need help with a few problems.

1.) (x^3/4 times y^1/3)^2/3

How is the answer x^1/2y^2/9

2.)(x^-1/3 times y) (x^1/2 times y^-4/3)
How is the answer x^1/6 over y^1/3

3.)(4a^2b^-7/2)^1/2
How is the answer 2a over b^3/4

4.) (x^2/3y^-1/3 over 8x^1/2y)^1/3
How is the answer x^1/18 over 2y^4/9

5.)(50x^3/4y/2x^1/2)+(x^1/2y^1/2/9x^3/4y^3/2)^-1/2

How is the answer 8x^1/8y^1/2

Please help explain so I can understand. Thank you!

  • (Math)Simplifying using the laws of exponents -

    multiply: add exponents
    raise to power: multiply exponents

    (x^3/4 y^1/3)^2/3
    = x^(3/4*2/3) y^(1/3*2/3)
    = x^1/2 y^2/9

    (x^-1/3 y)(x^1/2 y^-4/3)
    = x^(-1/3 + 1/2) y^(1 - 4/3)
    = x^1/6 y^-1/3
    = x^1/6 / y^1/3

    (4a^2 b^-7/2)^1/2
    = 4^1/2 a^(2*1/2) b^(-7/2*1/2)
    = 2a b^(-7/4)
    = 2a / b^7/4
    Given answer is wrong

    (x^2/3 y^-1/3 / 8x^1/2 y)^1/3
    = (x^(2/3 - 1/2) y^(-1/3 - 1) / 8)^1/3
    = x^1/18 / 2y^4/9

    Just keep track of the details, and make sure your arithmetic is as good as your algebra!

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