fully simplify using only positive exponents. $\frac{125x^{7}y^{5}}{25x^{8}y^{7}}$

Explanation:

Step1: Simplify the coefficient

$\frac{125}{25}=5$

Step2: Use the quotient - rule for exponents $a^m\div a^n=a^{m - n}$ for $x$ terms

$\frac{x^{7}}{x^{8}}=x^{7-8}=x^{-1}=\frac{1}{x}$

Step3: Use the quotient - rule for exponents for $y$ terms

$\frac{y^{5}}{y^{7}}=y^{5 - 7}=y^{-2}=\frac{1}{y^{2}}$

Step4: Combine the results

$5\times\frac{1}{x}\times\frac{1}{y^{2}}=\frac{5}{xy^{2}}$

Answer:

$\frac{5}{xy^{2}}$