Simplify and write the answer with only positive exponents

Question

(X^-3)²(x^-5)^-3

——————

(x^-3)^-5

^divide

Answer 1

One possible approach is

Step 1:You can use the exponent rule (a^m)ⁿ = a^mn in the numerator and the denominator.

Step2: Use the exponent rules a^-m = 1 / a^m OR 1/a^-n = aⁿ as needed to make all your exponents positive.

Step 3: Then use the exponent rules a^m x aⁿ = a^m+n OR a^m /aⁿ = a^m-n as needed.

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Answer 2

1/x^6

(x^-5)^-3 = x^15 which = (x^-3)^-5

they cancel leaving only (x^-3)^2 = x^-6 = 1/x^6