Q:

Which of the following is equivalent to (16^3/2)^1/2? 6 8 12 64

Accepted Solution

A:
[tex]\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad \sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\ -------------------------------\\\\ \left( 16^{\frac{3}{2}} \right)^{\frac{1}{2}}\implies 16^{\frac{3}{2}\cdot \frac{1}{2}}\implies 16^{\frac{3}{4}}\qquad \boxed{16=2^4}\qquad (2^4)^{\frac{3}{4}}\implies 2^{4\cdot \frac{3}{4}} \\\\\\ 2^3\implies 8[/tex]