Question

1. fully simplify using only positive exponents. $\frac{9x^{2}y^{7}}{x^{8}y^{4}}$

Explanation:

Step1: Use exponent - division rule for $x$ terms

When dividing terms with the same base $a^m\div a^n=a^{m - n}$. For the $x$ terms, we have $x^{2}\div x^{8}=x^{2-8}=x^{- 6}=\frac{1}{x^{6}}$.

Step2: Use exponent - division rule for $y$ terms

For the $y$ terms, $y^{7}\div y^{4}=y^{7 - 4}=y^{3}$.

Step3: Combine the results

The original expression $\frac{9x^{2}y^{7}}{x^{8}y^{4}}=9\times\frac{x^{2}}{x^{8}}\times\frac{y^{7}}{y^{4}}$. Substituting the results from step 1 and step 2, we get $9\times\frac{1}{x^{6}}\times y^{3}=\frac{9y^{3}}{x^{6}}$.

Answer:

$\frac{9y^{3}}{x^{6}}$