Question

Which is equivalent to 5 Square root of 1215^x

Answer 1

Answer:

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

Step-by-step explanation:

Given that

$\sqrt[5]{1215^{x} }$

=> $1215^{\frac{x}{5} }$ Using radical rule

=> $(3*3*3*3*3*5)^{\frac{x}{5} }$

=> $(3^{5} * 5 )^{\frac{x}{5} }$

=> $(3^{5*\frac{1}{5} } * 5 )^{x}$

=> $(3*5^{\frac{1}{5} } )^{x}$

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

Answer 2

Answer:

$5\sqrt{1215^{x}}\Rightarrow 45\sqrt{15^{x}}\:\:or\:\:45*15^{\frac{x}{2}}$

Step-by-step 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:

$45\sqrt{15^{x}}\:\:=\:\:45*15^{\frac{x}{2}}$