Intermediate Algebra, Chapter 5, 5.1, Section 5.1, Problem 52

Write the expression $6^{-1}-4^{-1}$ with only positive exponents. Then, simplify the expression.
Remove the negative exponent by rewriting $6^{-1}$ as $\dfrac{1}{6}$. A negative exponent follows the rule of $a^{-n} = \dfrac{1}{a^n}$
$\dfrac{1}{6}-4^{-1}$
Remove the negative exponent by rewriting $4^{-1}$ as $\dfrac{1}{4}$. A negative exponent follows the rule of $a^{-n} = \dfrac{1}{a^n}$
$\dfrac{1}{6}-\dfrac{1}{4}$

To subtract 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 $12$. Next, multiply each fraction by a factor of $1$ that will create the LCD in each of the fractions.
$\dfrac{1}{6}\cdot\dfrac{2}{2}-\dfrac{1}{4}\cdot\dfrac{3}{3}$
Complete the multiplication to produce a denominator of $12$ in each expression.
$\dfrac{2}{12}-\dfrac{3}{12}$
Combine the numerators of all fractions that have common denominators.
$\dfrac{1}{12}(2-3)$
Subtract $2$ to $3$ to get $-1$
$\dfrac{-1}{12}$