Question

Which is equivalent to 216 power of 1/3 ?
3
6
36
72

Answer 1

Option (b) is correct.

`(216)^{(1)/(3)}=6`

Explanation:

Given: 216 power of 1/3

We have to find an equivalent number to 216 power of 1/3

Consider 216 power of 1/3

Writing mathematically as,
`(216)^{(1)/(3) }`

Also, 216 can be written as product of 6 three times that is 6× 6 × 6

Thus,
`(216)^{(1)/(3)}=(6* 6* 6)^{(1)/(3)}`

Simplify, we get,

`(6* 6* 6)^{(1)/(3)}=(6^3)^{(1)/(3)}`

Apply property of exponents, we have,

`(a^n)^m=a^(nm)`

`(6^3)^{(1)/(3)}=6^{(3)/(3)}=6`

Thus,
`(216)^{(1)/(3)}=6`

Option (b) is correct.

Answer 2

6

Explanation:

GIVEN :

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

Solution :

let

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

`216 = x^(3)`

`6^(3) = x^(3)`

⇒ x = 6

⇒
`(216)^{(1)/(3) }= 6`