# How do you multiply (2a ^ { - 2} ) ^ { 3} ( a ^ { 4} a ^ { - 5} ) ^ { 6}?

Jul 10, 2018

$\frac{8}{a} ^ \left(12\right)$

#### Explanation:

We have ${\left(2 {a}^{- 2}\right)}^{3} {\left({a}^{4} \cdot {a}^{- 5}\right)}^{6}$
Note that ${a}^{4} \cdot {a}^{- 5} = {a}^{- 1}$
and ${\left(a b\right)}^{n} = {a}^{n} \cdot {b}^{n}$ so we get

${2}^{3} \cdot {a}^{- 6} \cdot {a}^{- 6} = 8 \cdot {a}^{- 12} = \frac{8}{a} ^ 12$

$\frac{8}{a} ^ 12$

#### Explanation:

Given tha

${\left(2 {a}^{- 2}\right)}^{3} {\left({a}^{4} {a}^{- 5}\right)}^{6}$

$= {2}^{3} {a}^{- 2 \setminus \cdot 3} {\left({a}^{- 5 + 4}\right)}^{6}$

$= 8 {a}^{- 6} {\left({a}^{- 1}\right)}^{6}$

$= 8 {a}^{- 6} \setminus \cdot {a}^{- 6}$

$= 8 {a}^{- 6 - 6}$

$= 8 {a}^{- 12}$

$= \frac{8}{a} ^ 12$