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

2 Answers
Nov 23, 2017

here a=2

Explanation:

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

Nov 23, 2017

a = 2

Explanation:

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!