How do you simplify 2m^-2 and write it using only positive exponents?

Oct 16, 2016

$2 \cdot \frac{1}{m} ^ 2$

Explanation:

The thing to remember about exponents is that they essentially switch signs every time you move terms from one side of the fraction bar to the other, i.e. from the numerator to the denominator, or vice versa.

Take, for example, $2$. As you know, this can be written as

$2 = \frac{2}{1} = {2}^{1} / 1$

If you want to write $2$ with a negative exponent, you have to do two things

• move $2$ from the numerator of ${2}^{1} / 1$ to the denominator
• switch the sign of its exponent

You would have

${2}^{1} / 1 = \frac{1}{2} ^ \textcolor{red}{- 1}$

Now try this for ${m}^{- 2}$. To write it using a positive exponent, you must move $m$ from the numerator of ${m}^{- 2} / 1$ to the denominator and switch its sign.

${m}^{- 2} = \frac{1}{m} ^ \textcolor{red}{2}$

And there you have it. Put it all together to find

$2 \cdot {m}^{- 2} = 2 \cdot \frac{1}{m} ^ \left(2\right)$

Do one more for good practice. How would you write ${a}^{- 2} / 3$ using only positive exponents?

Move $a$ from the numerator to the denominator and switch its sign -- keep in mind that $3$ already has a positive exponent, ${3}^{1}$, so leave it as-is!

a^(-2)/3 = 1/3 * 1/a^color(red)(2) = 1/(3a^color(red)(2)