Question

Which is equivalent to 5 Square root of 1215^x

Answer 1

`(3\sqrt[5]{5} )^(x)`

Explanation:

Given that

`\sqrt[5]{1215^(x) }`

=>
`1215^{(x)/(5) }` Using radical rule

=>
`(3*3*3*3*3*5)^{(x)/(5) }`

=>
`(3^(5) * 5 )^{(x)/(5) }`

=>
`(3^{5*(1)/(5) } * 5 )^(x)`

=>
`(3*5^{(1)/(5) } )^(x)`

=>
`(3\sqrt[5]{5} )^(x)`

Answer 2

`5\sqrt{1215^(x)}\Rightarrow 45\sqrt{15^(x)}\:\:or\:\:45*15^{(x)/(2)}`

Explanation:

1) Performing Prime Factorization

`\\1215|3\\405|3\\135|3\\45|3\\15|3\\5|5\\1\Rightarrow 3^(2)*3^(3)*5`

2) Simplifying

`5\sqrt{3^(2)*3^(2)*3*5}\Rightarrow 5*9\sqrt{15^(x)}\Rightarrow 45\sqrt{15^(x)}`

3) Rewriting it as a power, where the denominator is the index, and the numerator is the exponent:

`45\sqrt{15^(x)}\:\:=\:\:45*15^{(x)/(2)}`