Respuesta :

absor201

Answer:

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

Step-by-step explanation:

Given that

[tex]\sqrt[5]{1215^{x} }[/tex]

=> [tex]1215^{\frac{x}{5} }[/tex] Using radical rule

=> [tex](3*3*3*3*3*5)^{\frac{x}{5} }[/tex]

=> [tex](3^{5} * 5 )^{\frac{x}{5} }[/tex]

=> [tex](3^{5*\frac{1}{5} } * 5 )^{x}[/tex]

=> [tex](3*5^{\frac{1}{5} } )^{x}[/tex]

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

profantoniofonte

Answer:

[tex]5\sqrt{1215^{x}}\Rightarrow 45\sqrt{15^{x}}\:\:or\:\:45*15^{\frac{x}{2}}[/tex]

Step-by-step explanation:

1) Performing Prime Factorization

[tex]\\1215|3\\405|3\\135|3\\45|3\\15|3\\5|5\\1\Rightarrow 3^{2}*3^{3}*5[/tex]

2) Simplifying

[tex]5\sqrt{3^{2}*3^{2}*3*5}\Rightarrow 5*9\sqrt{15^{x}}\Rightarrow 45\sqrt{15^{x}}[/tex]

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

[tex]45\sqrt{15^{x}}\:\:=\:\:45*15^{\frac{x}{2}}[/tex]

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