Answer :
Answer:
[tex]\boxed{\bold{3^{\frac{2}{15}}}}[/tex]
Explanation:
[tex]\bold{3^{2\cdot \frac{1}{5}}: \ 3^{\frac{2}{5}}}[/tex]
= [tex]\bold{\left(3^{\frac{2}{5}}\right)^{\frac{1}{3}}}[/tex]
Apply exponent rule [tex]\bold{\left(a^b\right)^c=a^{bc}}[/tex]
= [tex]\bold{3^{\frac{2}{5}\cdot \frac{1}{3}}}[/tex]
[tex]\bold{\frac{2}{5}\cdot \frac{1}{3} \ = \ \frac{2}{15} }[/tex]
[tex]\bold{3^{\frac{2}{15}}}[/tex]
The expression [tex](\sqrt[5]{3^2} )^{\frac{1}{3}[/tex] is equivalent to [tex]3^{\frac{2}{15}[/tex].
We have to determine, Which expression is equivalent to [tex](\sqrt[5]{3^2} )^{\frac{1}{3}[/tex].
To determine the value of the expression following all the steps given below.
Expression; [tex](\sqrt[5]{3^2} )^{\frac{1}{3}[/tex]
The power of a number is known as the exponent. It is usually expressed as a raised number or raised symbol.
By applying the exponent rule given expression is written as;
[tex]=(a^b)^c = a ^{bc}\\\\=(3^\frac{2}{5})^{\frac{1}{3}}\\\\= 3 ^{ \frac{2}{5}\times \frac{1}{3}}\\\\= 3^{\frac{2}{15}[/tex]
Hence, The expression [tex](\sqrt[5]{3^2} )^{\frac{1}{3}[/tex] is equivalent to [tex]3^{\frac{2}{15}[/tex].
To know more about Exponential function click the link given below.
https://brainly.com/question/2406524