Question

Can you check the following questions,please?

Simplify
30. (-2y)^0/(3x^2)^-3
= 1/(3^-3)(x^-6)
= 1/-27x^-6
= 27x^6

42. (-7x^5/14y^3)^3
= (-1^3)(x^15)/(2^3)(y^9)
= (-1x^15)/8y^9

Answer 1

#30 Your answer is fine, but line 3 has a spurious "-" in -27. Either it was a typo, or you lost it by accident. In any case, 3^-3 = 27, not -27.

Your other syntax is also mangled.

1/((3^-3)(x^-6))
= 1/(1/27 x^-6)
= 27x^6

Your mixing up fractions and negative exponents can cause confusion. I'd have nixed the negative exponents right up front:

1/(3x^2)^-3
= (3x^2)^3
= 27x^6

#42: again correct, but all those factors being cubed confuses me.
(-7x^5/14y^3)^3
= (-x^5/2y^3)^3
= -x^15/8y^9

Answer 2

Thanks for showing how you got rid of the negative exponent on #30. As for #42, that's just how it was on the worksheet. Thanks again.