Answer:
Option 1: [tex]\frac{2x}{3y^{2}z}[/tex]
Step-by-step explanation:
Using the Quotient Rule of Exponents:
[tex]\frac{a^{m}}{a^{n}} = a^{(m - n)}[/tex]
We could simplify the given exponential expression by reducing the constants and subtracting the exponents of the same base.
[tex]\frac{18x^{2}y}{27xy^{3}z}[/tex]
[tex]\frac{9*2*x^{2}y}{9*3*xy^{3}z}[/tex] = [tex]\frac{2x^{2}y}{3xy^{3}z}[/tex]
Subtract the exponents of x, which eliminates x from the denominator.
[tex]\frac{2xy}{3y^{3}z}[/tex]
Lastly, subtract the exponents of y. This process eliminates y from the numerator and leaving y² in the denominator.
[tex]\frac{2x}{3y^{2}z}[/tex] ⇒ This is the simplified form of the given exponential expression. Therefore, the correct answer is Option 1.
