Question

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

Answer 1

$3^2\cdot\sqrt{3^5}\qquad\text{use}\ \sqrt[n]{a^m}=a^{\frac{m}{n}}\\\\=3^2\cdot3^{\frac{5}{2}}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=3^{2+\frac{5}{2}}=3^{\frac{4}{2}+\frac{5}{2}}=3^{\frac{4+5}{2}}=3^{\frac{9}{2}}$