# How do you write x^11*x^-3 using only positive exponents?

Mar 29, 2018

${x}^{8}$

#### Explanation:

In general, you will use 4 common rules with exponents when solving these types of problems.

${x}^{n} \cdot {x}^{m} = {x}^{n + m}$
${x}^{-} a = \frac{1}{x} ^ a$ , similarly ${x}^{a} = \frac{1}{x} ^ - a$
${x}^{k} / {x}^{l} = {x}^{k - l}$
${\left({x}^{c}\right)}^{d} = {x}^{c \cdot d}$

Here is the most direct route using one exponential rule:

${x}^{n} \cdot {x}^{m} = {x}^{n + m}$

so,

${x}^{11} \cdot {x}^{-} 3 = {x}^{11 + \left(- 3\right)} = {x}^{8}$

Be playful, and you can figure out longer ways to get there too. Most of this type of stuff involves practice with the basic rules. You'll get it in no time once you solve a few. Good luck!

Mar 29, 2018

${x}^{8}$

#### Explanation:

We know that ${x}^{n} \cdot {x}^{m} = {x}^{n + m}$, and so,

${x}^{11} \cdot {x}^{-} 3$

$= {x}^{11 - 3}$

$= {x}^{8}$