# How do you write 5t^-3*3t^-8 using only positive exponents?

Feb 16, 2017

First, we can rewrite this expression as:

$\left(5 \cdot 3\right) \left({t}^{-} 3 \cdot {t}^{-} 8\right) = 15 \left({t}^{-} 3 \cdot {t}^{-} 8\right)$

Next, use this rule for exponents to combine the $t$ terms:

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

$15 \left({t}^{\textcolor{red}{- 3}} \times {t}^{\textcolor{b l u e}{- 8}}\right) = 15 {t}^{\textcolor{red}{- 3} + \textcolor{b l u e}{- 8}} = 15 {t}^{-} 11$

Now, use this rule for exponents to eliminate the negative exponent:

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

$15 {t}^{\textcolor{red}{- 11}} = \frac{15}{t} ^ \textcolor{red}{- - 11} = \frac{15}{t} ^ 11$