Question

Which expression is equivalent to -9x^-1y^-1 / -15x^5 y^-3 Assume x = 0 y = 0

Answer 1

`(-9x^(-1)y^(-1))/(-15x^5 y^(-3))\ \ \ \text{assume}\ x\\eq0\ \wedge\ y\\eq0\\\\\text{Use:}\\\\(a^n)/(a^m)=a^(n-m)\\\\a^(-n)=(1)/(a^n)`


`(-9x^(-1)y^(-1))/(-15x^5 y^(-3))=(-9:3)/(-15:3)\cdot x^(-1-5)y^(-1-(-3))=(3)/(5)\cdot x^(-6)y^(-1+3)\\\\=(3)/(5)\cdot(1)/(x^6)\cdot y^2=\boxed{(3y^2)/(5x^6)}`

Answer 2

For this case we have the following expression:
-9x ^ -1y ^ -1 / -15x ^ 5 y ^ -3
For power properties we have:
-9x ^ (- 1-5) y ^ (- 1 - (- 3)) / - 15
Rewriting we have:
9x ^ (- 6) y ^ (- 1 + 3) / 15
3x ^ (- 6) y ^ (2) / 5
3y ^ 2 / 5x ^ 6
Answer:
3y ^ 2 / 5x ^ 6Note: answer is not between the options. Rewrite the expression again, or the options.