## College Algebra (11th Edition)

$\dfrac{1}{12}$
$\bf{\text{Solution Outline:}}$ Use the laws of exponents to simplify the given expression, $3^{-1}-4^{-1} .$ Then change the resulting fractions to similar fractions. $\bf{\text{Solution Details:}}$ Using the Negative Exponent Rule of the laws of exponents which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{1}{3^1}-\dfrac{1}{4^1} \\\\= \dfrac{1}{3}-\dfrac{1}{4} .\end{array} To subtract the expression above, make the fractions similar (same denominator) by multiplying each term by an expression equal to $1$. The expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{1}{3}\cdot\dfrac{4}{4}-\dfrac{1}{4}\cdot\dfrac{3}{3} \\\\= \dfrac{4}{12}-\dfrac{3}{12} \\\\= \dfrac{4-3}{12} \\\\= \dfrac{1}{12} .\end{array}