Question

Simplify the square of 3 times the square root of 3 to the power of 5.

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

Answer 1

`3^2\cdot√(3^5)\qquad\text{use}\ \sqrt[n]{a^m}=a^{(m)/(n)}\\\\=3^2\cdot3^{(5)/(2)}\qquad\text{use}\ a^n\cdot a^m=a^(n+m)\\\\=3^{2+(5)/(2)}=3^{(4)/(2)+(5)/(2)}=3^{(4+5)/(2)}=3^{(9)/(2)}`