# How do you simplify -2^-1+5^-2?

Apr 3, 2018

$- \frac{23}{50}$

#### Explanation:

You just need to know how negative exponents work: they are the same as positive exponents, except for the fact that you have to "flip" the number before (i.e. swap numerator and denominator, where you can reed integers as divided by $1$).

For example, if you have ${2}^{- 1}$, you have to

flip the number: $2 = \frac{2}{1} \to \frac{1}{2}$

apply the positive power: ${\left(\frac{1}{2}\right)}^{1} = \frac{1}{2}$

While for ${5}^{- 2}$, you have to

flip the number: $5 = \frac{5}{1} \to \frac{1}{5}$

apply the positive power: ${\left(\frac{1}{5}\right)}^{2} = \frac{1}{25}$

Thus, we have

#-2^(-1) + 5^(-2) = -1/2+1/25 = (-25+2)/50 = -23/50