# How do you write 5^-8*5^-7 using only positive exponents?

Feb 10, 2017

First, we will use this rule of exponents to combine the $5$ terms:

${x}^{\textcolor{red}{a}} \times {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} + \textcolor{b l u e}{b}}$

${5}^{\textcolor{red}{- 8}} \times {5}^{\textcolor{b l u e}{- 7}} = {5}^{\textcolor{red}{- 8} + \textcolor{b l u e}{- 7}} = {5}^{-} 15$

Now, we can use this rule of exponents to eliminate the negative exponent:

${x}^{\textcolor{red}{a}} = \frac{1}{x} ^ \textcolor{red}{- a}$

${5}^{\textcolor{red}{- 15}} = \frac{1}{5} ^ \textcolor{red}{- - 15} = \frac{1}{5} ^ 15$