# How do you solve -5+ ( - 4- n ) ^ { - \frac { 3} { 2} } = - \frac { 39} { 8}?

Nov 28, 2017

Solution: $n = - 8$

#### Explanation:

$- 5 + {\left(- 4 - n\right)}^{- \frac{3}{2}} = - \frac{39}{8}$ or

$\frac{1}{- {\left(4 + n\right)}^{\frac{3}{2}}} = 5 - \frac{39}{8}$ or

$\frac{1}{- {\left(4 + n\right)}^{\frac{3}{2}}} = \frac{1}{8}$ or

$- {\left(4 + n\right)}^{\frac{3}{2}} = 8 \left[{4}^{\frac{3}{2}} = 8\right]$

$\therefore - {\left(4 + n\right)}^{\frac{3}{2}} = {4}^{\frac{3}{2}}$

$\therefore - \left(4 + n\right) = 4 \mathmr{and} n = - 4 - 4 = - 8$

Solution: $n = - 8$ [Ans]