Question

(10x^3y^-2/5x^-3y^4)^-3, x≠0, y≠0

Answer 1

Answer:

  $\dfrac{y^{18}}{8x^{18}}$

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  a^-b = 1/a^b

  (a^b)^c = a^(bc)

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Your expression simplifies as follows:

  $\left(\dfrac{10x^3y^{-2}}{5x^{-3}y^4}\right)^{-3}=(2x^{3-(-3)}y^{-2-4})^{-3}=(2x^6y^{-6})^{-3}\\\\=(2^{-3})x^{6(-3)}y^{(-6)(-3)}=\dfrac{1}{8}x^{-18}y^{18}\\\\=\boxed{\dfrac{y^{18}}{8x^{18}}}$