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simplify (xy)^-3/(x^-5 y)^3

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Kyle M. | Certified Educator with Masters, Tutoring 3rd Grade Through CollegeCertified Educator with Masters, Tutorin...
4.9 4.9 (169 lesson ratings) (169)
This one is more difficult & I'm perhaps less confident, but here goes:
Remember that negative exponents simply mean that the number & exponent become the denominator, with a one as the numerator. Thus (xy)^-3 is the same as 1/(xy)^3. Next, (x^-5 y)^3 should be multiplied out. Remember that we add exponents together when multiplying, so x^-5 times x^-5 times x^-5 becomes x^-15 or 1/x^15; the other variable becomes y^3. Now, that gives us y^3/x^15.
Next, let's write it out as division: 1/(xy)^3 divided by y^3/x^15. We invert the second term & multiply, so that we then have 1/(xy)^3 times x^15/y^3. Therefore we arrive at x^15/(xy)^3(y)^3. (xy)^3 is the same as x^3 times y^3, which we then multiply by y^3 - giving us x^3 times y^6. Finally, we have x^15/(x^3)(y^6) & we factor out the x^3 from the denominator & numerator (x^15), giving us x^12/y^6 - your final answer. Whew! I hope I did that correctly...