#### Answer

$\dfrac{25}{6}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To multiply the given expression, $
\dfrac{15}{14}\cdot\dfrac{35}{9}
,$ cancel the common factors between the numerator and the denominator. Then multiply the numerators and multiply the denominators.
$\bf{\text{Solution Details:}}$
Cancelling the common factors between the numerator and the denominator, the given expression is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{15}{14}\cdot\dfrac{35}{9}
\\\\=
\dfrac{\cancel3(5)}{\cancel7(2)}\cdot\dfrac{\cancel7(5)}{\cancel3(3)}
\\\\=
\dfrac{5}{2}\cdot\dfrac{5}{3}
.\end{array}
To multiply fractions, multiply the numerators and multiply the denominators. Hence, the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{5}{2}\cdot\dfrac{5}{3}
\\\\=
\dfrac{5(5)}{2(3)}
\\\\=
\dfrac{25}{6}
.\end{array}