Intermediate Algebra, Chapter 5, 5.1, Section 5.1, Problem 49

Write the expression $5^{-1}+6^{-1}$ with only positive exponents. Then, simplify the expression.
Remove the negative exponent by rewriting $5^{-1}$ as $\dfrac{1}{5}$. A negative exponent follows the rule of $a^{-n} = \dfrac{1}{a^n}$
$\dfrac{1}{5}+6^{-1}$
Remove the negative exponent by rewriting $6^{-1}$ as $\dfrac{1}{6}$. A negative exponent follows the rule of $a^{-n} = \dfrac{1}{a^n}$
$\dfrac{1}{5}+\dfrac{1}{6}$

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 $30$. Next, multiply each fraction by a factor of $1$ that will create the LCD in each of the fractions.
$\dfrac{1}{5}\cdot\dfrac{6}{6}+\dfrac{1}{6}\cdot\dfrac{5}{5}$
Complete the multiplication to produce a denominator of $30$ in each expression.
$\dfrac{6}{30}+\dfrac{5}{30}$
Combine the numerators of all fractions that have common denominators.
$\dfrac{1}{30}(6+5)$
Add $5$ to $6$ to get $11$
$\dfrac{11}{30}$