# How do you write 2^-3/2^4 using only positive exponents?

Sep 4, 2016

$\frac{1}{2} ^ 7$

#### Explanation:

There are 2 laws of indices that we can use here.

Subtract the indices, or to get rid of the negative index,

2^-3/2^4 = 1/(2^(4-(-3))

=$\frac{1}{2} ^ 7$

OR

${2}^{-} \frac{3}{2} ^ 4 = \frac{1}{{2}^{4} \times {2}^{3}}$

=$\frac{1}{2} ^ 7$

Sep 4, 2016

We have: $\frac{{2}^{- 3}}{{2}^{4}}$

Using the laws of exponents:

$= {2}^{- 3 - 4}$

$= {2}^{- 7}$

$= \frac{1}{{2}^{7}}$