# How do you write 3^-5 using only positive exponents?

Oct 5, 2016

${3}^{-} 5 = \frac{1}{3} ^ 5$

#### Explanation:

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

${3}^{-} 5 = \frac{1}{3} ^ 5$

The index is now positive.

We could carry on and show that it simplifies to $\frac{1}{243}$, but this would usually not be necessary.