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ozzi
3 years ago
6

Which is equivalent to 5 Square root of 1215^x

Mathematics
2 answers:
tia_tia [17]3 years ago
8 0

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}

drek231 [11]3 years ago
3 0

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}}

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