\
"One way to do this is as below. The main tool used here is the"
"Subtraction Rule for Exponents."
"Here we go:"
{ y^5 x^3 } / { y^5 x^3 } \ = \ y^5/y^5 \cdot x^3 / x^4 \ = \ y^{ 5 - 5 } \cdot x^{ 3 - 4 } \qquad \qquad \qquad \qquad \quad "Subtraction Rule"
\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad = \ y^{ 0 } \cdot x^{ -1 }
\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad = \1 \cdot x^{ -1 } \qquad \qquad \qquad \quad "Zero Exponent Definition"
\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad = x^{ -1 }
\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad = 1 / x \quad. \qquad \quad \quad \ "Negative Exponent Definition"
"This is our answer."
\
"Summarizing:"
\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ { y^5 x^3 } / { y^5 x^4 } \ = \ x^{ -1 } \quad.