Question

The value of the expression 16^-3/4 is ______

Answer 1

$\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\ \rule{31em}{0.25pt} \\\\ 16^{-\frac{3}{4}}\implies \cfrac{1}{16^{\frac{3}{4}}}~~ \begin{cases} 16=2\cdot 2\cdot 2\cdot 2\\ \qquad 2^4 \end{cases}\implies \cfrac{1}{(2^4)^{\frac{3}{4}}}\implies \cfrac{1}{2^3}\implies \cfrac{1}{8}$