Question

Simplify (−5p^3)^3, (−w^3/6)^−2, (1/2r^6)^-6, (4s^5t^−7/−2s^−2t^4)^3, and (3x^3y^0x*−2)^4⋅(y^2x^−4^5xy^−8)^3.

Answer 1

`Use:\\\\(ab)^n=a^nb^n\\\\\left((a)/(b)\right)^n=(a^n)/(b^n)\\\\(a^n)^m=a^(nm)\\\\(a^n)/(a^m)=a^(n-m)\\\\a^n\cdot a^m=a^(n+m)\\\\a^(-n)=(1)/(a^n)\\--------------------------------`

`(-5p^3)^3=(-5)^3(p^3)^3=-125p^((3)(3))=-125p^9\\\\\left(-(w^3)/(6)\right)^(-2)\right)=\left(-(6)/(w^3)\right)^2=\left((6)/(w^3)\right)^2=(6^2)/((w^3)^2)=(36)/(w^((3)(2)))=(36)/(w^6)\\\\\left((1)/(2r^6)\right)^(-6)=(2r^6)^6=2^6(r^6)^6=64r^((6)(6))=64r^(36)\\\\\left((4s^5t^(-7))/(-2s^(-2)t^4)\right)^3=\left(-(4)/(2)s^(5-(-2))t^(-7-4)\right)^3=\left(-2s^7t^(-11)\right)^3\\\\=(-2)^3(s^7)^3(t^(-11))^3=-8s^(21)t^(-33)`

`(3x^3y^0x^(-2))^4(y^2x^(-4^5)xy^(-8))^3=(3x^(3+(-2))1)^4(y^(2+(-8))x^(-1024+1))^3.`

`=(3x^1)^4(y^(-6)x^(-1023))^3=3^4x^4(y^(-6))^3(x^(-1023))^3=81x^4y^(-18)x^(-3069)\\\\=81x^(4+(-3069))y^(-18)=81x^(-3065)y^(-18)`