# How do you simplify (2^-1)^2/2^4 and write it using only positive exponents?

May 12, 2018

Answer is $\frac{1}{2} ^ 6$

#### Explanation:

By using exponential law:
${a}^{-} 1 = \frac{1}{a}$

So, ${2}^{- 1} = \frac{1}{2}$
${\left({2}^{- 1}\right)}^{2} = {\left(\frac{1}{2}\right)}^{2}$ = $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$

So now we get;
$\frac{\frac{1}{4}}{2} ^ 4$ = $\frac{1}{4} \times \frac{1}{2} ^ 4$ = $\frac{1}{4} \times \frac{1}{16} = \frac{1}{64}$ = $\frac{1}{2} ^ 6$