Question

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If the expression
`(3^a*√(6) )/(9*√(54) )` is equal to 1, what is the value of a?


A. 1

B. 2

C.3

D.4

Answer 1

`C.3`

Explanation:

`We\ are\ given:\\(3^a*√(6) )/(9*√(54))=1\\Hence,\\By\ using\ one\ of\ the\ Laws\ of\ Exponents:[(x^a)/(y^a)]=[(x)/(y)]^a\\Hence,\\(3^a*√(6) )/(9*√(54) )=1\\ (3^a)/(9)*(√(6) )/(√(54) ) =1\\Hence,\\(3^a)/(9)*\sqrt{(6)/(54) }=1\\ (3^a)/(9)*\sqrt{(1)/(9) }=1\\(3^a)/(9)*(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`