Write the expression $2^{-1}+8^{-1}$ with only positive exponents. Then, simplify the expression.
Remove the negative exponent by rewriting $2^{-1}$ as $\dfrac{1}{2}$. A negative exponent follows the rule of $a^{-n} = \dfrac{1}{a^n}$
$\dfrac{1}{2}+8^{-1}$
Remove the negative exponent by rewriting $8^{-1}$ as $\dfrac{1}{8}$. A negative exponent follows the rule of $a^{-n} = \dfrac{1}{a^n}$
$\dfrac{1}{2}+\dfrac{1}{8}$
To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is $8$. Next, multiply each fraction by a factor of $1$ that will create the LCD in each of the fractions.
$\dfrac{1}{2}\cdot\dfrac{4}{4}+\dfrac{1}{8}\cdot\dfrac{1}{1}$
Complete the multiplication to produce a denominator of $8$ in each expression.
$\dfrac{4}{8}+\dfrac{1}{8}$
Combine the numerators of all fractions that have common denominators.
$\dfrac{1}{8}(4+1)$
Add $4$ to $1$ to get $5$
$\dfrac{5}{8}$
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