Question

fully simplify using only positive exponents.
$\frac{27xy^{3}}{3x^{8}y^{7}}$

Explanation:

Step1: Simplify the coefficient

Divide 27 by 3: $\frac{27}{3}=9$.

Step2: Use the quotient - rule for exponents

For $x$ terms, $\frac{x}{x^{8}}=x^{1 - 8}=x^{-7}=\frac{1}{x^{7}}$ (using $a^{m}\div a^{n}=a^{m - n}$).
For $y$ terms, $\frac{y^{3}}{y^{7}}=y^{3 - 7}=y^{-4}=\frac{1}{y^{4}}$.

Step3: Combine the results

The simplified expression is $9\times\frac{1}{x^{7}}\times\frac{1}{y^{4}}=\frac{9}{x^{7}y^{4}}$.

Answer:

$\frac{9}{x^{7}y^{4}}$