Find the area of the rectangle. (2a^2b)/(c^5) (c^3)/(6ab)

To find the area of the rectangle, we need to multiply the length and width of the rectangle.<br /><br />Given:<br />Length = $\frac {2a^{2}b}{c^{5}}$<br />Width = $\frac {c^{3}}{6ab}$<br /><br />To multiply these fractions, we multiply the numerators together and the denominators together:<br /><br />$\frac {2a^{2}b}{c^{5}} \times \frac {c^{3}}{6ab} = \frac {2a^{2}b \cdot c^{3}}{c^{5} \cdot 6ab}$<br /><br />Simplifying the expression, we get:<br /><br />$\frac {2a^{2}b \cdot c^{3}}{c^{5} \cdot 6ab} = \frac {2a^{2}c^{3}}{6ac^{5}}$<br /><br />Now, we can cancel out the common factors in the numerator and denominator:<br /><br />$\frac {2a^{2}c^{3}}{6ac^{5}} = \frac {2a \cdot c^{3}}{6c^{5}}$<br /><br />Simplifying further, we get:<br /><br />$\frac {2a \cdot c^{3}}{6c^{5}} = \frac {a}{3c^{2}}$<br /><br />Therefore, the area of the rectangle is $\frac {a}{3c^{2}}$.