Answer:
[tex]C.3[/tex]
Step-by-step explanation:
[tex]We\ are\ given:\\\frac{3^a*\sqrt{6} }{9*\sqrt{54}}=1\\Hence,\\By\ using\ one\ of\ the\ Laws\ of\ Exponents:[\frac{x^a}{y^a}]=[\frac{x}{y}]^a\\Hence,\\\frac{3^a*\sqrt{6} }{9*\sqrt{54} }=1\\ \frac{3^a}{9}*\frac{\sqrt{6} }{\sqrt{54} } =1\\Hence,\\\frac{3^a}{9}*\sqrt{\frac{6}{54} }=1\\ \frac{3^a}{9}*\sqrt{\frac{1}{9} }=1\\\frac{3^a}{9}*\frac{1}{3}=1\\\\3^a=3*9\\3^a=27\\3^a=3^3\\As\ the\ bases(3)\ is\ equal,\ the\ exponents\ are\ equal\ too.\\Hence,\\a=3[/tex]
