Question

Simplify (√3)(^5√3)

A. 3^1/10
B. 3^3/5
C. 3^9/10
D. 3^7/10

Answer 1

`\sqrt[n]{a}=a^{(1)/(n)}\\\\\text{Therefore}\\\\\sqrt3=3^(1)/(2)\\\\\sqrt[5]{3}=3^(1)/(5)\\\\\text{We have}\\\\(\sqrt3)(\sqrt[5]3)=3^(1)/(2)\cdot3^(1)/(5)\qquad\text{use}\ a^n\cdot a^m=a^(n+m)\\\\=3^{(1)/(2)+(1)/(5)}=3^{(5)/(10)+(2)/(10)}=3^{(7)/(10)}\\\\Answer:\ \boxed{D.\ 3^{(7)/(10)}}`