Question

How do u solve this?

Answer 1

`6r^3`

Explanation:

`\left(216r^9\right)^{(1)/(3)}`

Apply exponent rule:
`\left(a* \:b\right)^n=a^nb^n`

`\longmapsto`
`\left(216r^9\right)^{(1)/(3)}=216^{(1)/(3)}\left(r^9\right)^{(1)/(3)}`

`\longmapsto216^{(1)/(3)}\left(r^9\right)^{(1)/(3)}`

`216^{(1)/(3)}`

Factor 216 = 6³

`\longmapsto \left(6^3\right)^{(1)/(3)}`

Apply exponent rule:
`\left(a^b\right)^c=a^(bc),\:\quad \:a\ge 0`

`\longmapsto`
`\left(6^3\right)^{(1)/(3)}=6^{3\cdot (1)/(3)}`

`\longmapsto 6^{3\cdot (1)/(3)}`

`\longmapsto3* (1)/(3)=1`

`\longmapsto6^1`

`\longmapsto6`

`6\left(r^9\right)^{(1)/(3)}`

Apply exponent rule:
`\left(a^b\right)^c=a^(bc)`

`\longmapsto\left(r^9\right)^{(1)/(3)}=r^{9\cdot (1)/(3)}`

`\longmapsto6r^{9\cdot (1)/(3)}`

`\longmapsto9*(1)/(3) =3`

`\longmapsto6r^3`

________________________

OAmalOHopeO

Answer 2

216 = 6^3

_____________

( 6^3 r^9 )^ 1/3 =

( 6^3/3 ) × ( r^9/3 ) =

6 × r^3 =

6r^3