# Question #f6a1b

$a = \frac{27}{10}$

#### Explanation:

If the given equation is

${5}^{\frac{1}{5}} \cdot {5}^{3} / {5}^{- \frac{3}{2}} = {5}^{a + 2}$

then

${5}^{\frac{1}{5}} \cdot {5}^{3} \cdot {5}^{\frac{3}{2}} = {5}^{a + 2}$

${5}^{\frac{1}{5} + 3 + \frac{3}{2}} = {5}^{a + 2}$

if the bases are equal in an equation, then, exponents are equal also.

$\frac{1}{5} + 3 + \frac{3}{2} = a + 2$

solving for a:

$\frac{2 + 30 - 20 + 15}{10} = a$

$a = \frac{27}{10}$