Answer:
C
Step-by-step explanation:
First note that
[tex]\dfrac{1}{3}=\dfrac{5}{15}\Rightarrow x^{\frac{1}{3}}=x^{\frac{5}{15}};\\ \\\\\dfrac{1}{5}=\dfrac{3}{15}\Rightarrow y^{\frac{1}{5}}=y^{\frac{3}{15}}[/tex]
Now use the property
[tex]a^n\cdot b^n=(ab)^n,[/tex]
so
[tex]x^{\frac{5}{15}}\cdot y^{\frac{3}{15}}=(x^5)^{\frac{1}{15}}\cdot (y^3)^{\frac{1}{15}}=(x^5y^3)^{\frac{1}{15}}.[/tex]
Since [tex]a^{\frac{1}{15}}=\sqrt[15]{a},[/tex]
you have
[tex]15(x^5y^3)^{\frac{1}{15}}=15\sqrt[15]{x^5y^3} .[/tex]
