If the expression #(3^a * 2\sqrt 9)/ (27\sqrt 4) = 1#, what is the value of a?

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Answer 1 · 2017-11-23T15:00:44

here #a=2#

given, #(3^a.2sqrt(9))/(27sqrt(4))=1rArr(3^a.2.3)/27.2=1rArr3^(a+1)/27=1rArr3^(a+1)=27rArr3^(a+1)=3^3rArra+1=3rArra=2#

Answer 2 · 2017-11-23T15:36:50

#a = 2#

Find #a#

#(3^a⋅2√9)/(27√4) =1#

1) Find the square roots of 9 and 4

#(3^a⋅2*3)/(27*2) =1#

2) Cancel the 2 from the numerator and from the denominator
#(3^a⋅3)/(27) =1#

3) #(3^(a+1))/(27) =1#

4) Clear the fraction by multiplying both sides by 27 and letting the denominator cancel
#3^(a + 1) = 27#

5) Write 27 as #3^3#
#3^(a + 1) = 3^3#

6) The bases are both 3, so the exponents are equal
#a + 1 = 3#

7) Subtract 1 from both sides to isolate #a#
#a = 2 larr# answer

Answer:
a = 2
...................

Check
Sub in 2 for #a# in the original equation

Given #(3^a⋅2√9)/(27√4) =1#

Sub in 2
#(3^2⋅2√9)/(27√4) =1#

This is the same as
#(9*2*3)/(27*2)#
and it all should still equal 1

#(54)/(54)# does equal 1

Check!