# How do you write z^-5*z^-1 using only positive exponents?

Sep 30, 2016

$\frac{1}{z} ^ 6$

#### Explanation:

Recall: ${x}^{-} m = \frac{1}{x} ^ m$

There are two approaches - either:

add the indices first with one base and then attend to the negative index:

${z}^{-} 5 \times {z}^{-} 1 = {z}^{-} 6 = \frac{1}{z} ^ 6$

OR

Attend to the negative indices first, then add the indices.

${z}^{-} 5 \times {z}^{-} 1 = \frac{1}{z} ^ 5 \times \frac{1}{z} = \frac{1}{z} ^ 6$