Question

Evaluate this exponential expression (27/8)^ 4/3 A: 9/2 B: 4/3 C: 81/16

Answer 1

$\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left( \cfrac{27}{8} \right)^{\frac{4}{3}}\implies \left( \cfrac{3^3}{2^3} \right)^{\frac{4}{3}}\implies \left( \cfrac{3^{3\cdot \frac{4}{3}}}{2^{3\cdot \frac{4}{3}}} \right)\implies \cfrac{3^4}{2^4}\implies \cfrac{81}{16}$