## Elementary Algebra

$-\frac{2}{9}b^{2}$
Recall the following rule: $\frac{x^{m}}{x^{n}}=x^{m-n}$ We use this rule to help us cancel out common factors in the numerator and the denominator and obtain: $\frac{12a^{2}b^{5}}{-54a^{2}b^{3}}$ =$-\frac{12}{54}\times\frac{a^{2}}{a^{2}}\times\frac{b^{5}}{b^{3}}$ =$-\frac{6}{27}\times a^{2-2}\times b^{5-3}$ =$-\frac{2}{9}\times a^{0}\times b^{2}$ =$-\frac{2}{9}\times 1\times b^{2}$ [as $a^{0}=1$] =$-\frac{2}{9}b^{2}$