Question

Question #847b3

Answer 1

C. `9x^2`

Explanation:

`(27x^3)^(2/3)`= `root(3)((27x^3)^2)`

= `root(3)`( `729x^6` )
= `root(3)(729) * root(3)x^6`
`=9x^2`

Answer 2

`9x^2toC`

Explanation:

`"using the "color(blue)"laws of exponents"`

`•color(white)(x)(a^mb^n)^p=a^(mp)b^(np)`

`•color(white)(x)a^(m/n)=(root(n)(a))^m`

`rArr(27x^3)^(2/3)=27^(2/3)x^((3xx2/3))=27^(2/3)x^2`

`27^(2/3)=(root(3)(27))^2=3^2=9`

`rArr(27x^3)^(2/3)=9x^2toC`