Question

Which is equivalent to 243 2/5? 3 6 9 12

Answer 1

ANSWER


`{(243)}^{ (2)/(5) } = 9`


Step-by-step explanation

We want to simplify the exponential expression,



`{(243)}^{ (2)/(5) }`


We use the laws of indices to simplify the expression.



We rewrite the above expression to obtain,


`{(243)}^{ (2)/(5) } = {(243)}^{ (1)/(5) * 2 }`

Recall that,



`{a}^(mn) = ( {a}^(m) ) ^(n)`


When we apply the above property, we get


`{(243)}^{ (2)/(5) } = {( {(243)}^{ (1)/(5) } )}^(2)`


Now we need to write

`243`
as a certain number to the exponent of 5.



In order words,


`243 = 3 * 3 * 3 * 3 * 3 = {3}^(5)`



This implies that,



`{(243)}^{ (2)/(5) } = {( { {3}^(5) }^{ * (1)/(5) } )}^(2)`



We further simplify to get,



`{(243)}^{ (2)/(5) } = 3^(2)`


This will finally evaluate to,



`{(243)}^{ (2)/(5) } = 9`

Answer 2

`243^{ (2)/(5) } = ( \sqrt[5]{243} )^(2) = 3^(2) =9`