# How do you simplify ((2^3 •(2^2)^3)^2 )/ 2?

Jul 4, 2016

${\left({2}^{3} \cdot {\left({2}^{2}\right)}^{3}\right)}^{2} / 2 = {2}^{17}$

#### Explanation:

We can use here three formulas relating to exponents;

${a}^{m} \cdot {a}^{n} = {a}^{\left(m + n\right)}$, ${a}^{m} / {a}^{n} = {a}^{\left(m - n\right)}$ and ${\left({a}^{m}\right)}^{n} = {a}^{\left(m \times n\right)}$

Hence ${\left({2}^{3} \cdot {\left({2}^{2}\right)}^{3}\right)}^{2} / 2$

= ${\left({2}^{3} \cdot {2}^{\left(2 \times 3\right)}\right)}^{2} / 2$

= ${\left({2}^{3} \cdot {2}^{6}\right)}^{2} / 2$

= ${\left({2}^{\left(3 + 6\right)}\right)}^{2} / 2$

= ${\left({2}^{9}\right)}^{2} / {2}^{1}$ (as $a = {a}^{1}$)

= ${2}^{\left(9 \times 2\right)} / {2}^{1}$

= ${2}^{18} / {2}^{1}$

= ${2}^{\left(18 - 1\right)}$

= ${2}^{17}$