# How do you simplify (2^5*2^-4)/2 and write it using only positive exponents?

Jan 3, 2018

1

#### Explanation:

Given $\frac{{2}^{5} \cdot {2}^{-} 4}{2}$.

First use the property that ${a}^{b} \cdot {a}^{c} = {a}^{b + c}$ in the numerator:

$\frac{{2}^{5} \cdot {2}^{-} 4}{2} = \frac{{2}^{5 + \left(- 4\right)}}{2} = {2}^{1} / 2$

${2}^{1} / 2 = \frac{2}{2} = 1$

Jan 3, 2018

$1$

#### Explanation:

$\text{using the "color(blue)"law of exponents}$

•color(white)(x)a^mxxa^n=a^((m+n))

•color(white)(x)a^0=1

$\Rightarrow \frac{{2}^{5} \times {2}^{- 4}}{2} = {2}^{\left(5 + \left(- 4\right)\right)} / 2 = {2}^{5 - 4} / {2}^{1} = {2}^{1} / {2}^{1} = {2}^{1 - 1} = {2}^{0} = 1$
Or simply
${2}^{1} / {2}^{1} = \frac{2}{2} = 1$