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

Nov 23, 2017

here $a = 2$

#### Explanation:

given, $\frac{{3}^{a} .2 \sqrt{9}}{27 \sqrt{4}} = 1 \Rightarrow \frac{{3}^{a} .2 .3}{27.2} = 1 \Rightarrow {3}^{a + 1} / 27 = 1 \Rightarrow {3}^{a + 1} = 27 \Rightarrow {3}^{a + 1} = {3}^{3} \Rightarrow a + 1 = 3 \Rightarrow a = 2$

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) $\frac{{3}^{a + 1}}{27} = 1$

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 $a$
$a = 2 \leftarrow$ 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
$\frac{9 \cdot 2 \cdot 3}{27 \cdot 2}$
and it all should still equal 1

$\frac{54}{54}$ does equal 1

Check!