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^{( n)/( m)} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-( n)/( m)} \implies \cfrac{1}{a^{( n)/( m)}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left( \cfrac{27}{8} \right)^{(4)/(3)}\implies \left( \cfrac{3^3}{2^3} \right)^{(4)/(3)}\implies \left( \cfrac{3^{3\cdot (4)/(3)}}{2^{3\cdot (4)/(3)}} \right)\implies \cfrac{3^4}{2^4}\implies \cfrac{81}{16}`