Simplify $\frac{8xy^2}{6x^2y}$ with $x=2$ and $y=3.$
First, we look for factors that are in both the numerator and the denominator. Since $6$ and $8$ are both even, we can take out a factor of $2.$ We can also cancel a factor of $x$ and a factor of $y$ since they each appear in both the numerator and the denominator. This leaves us with \[\frac{\cancelto{4}{8}\cancel{x}y^{\cancel{2}}}{\cancelto{3}{6}x^{\cancel{2}}\cancel{y}}=\frac{4y}{3x}.\]Now we substitute $x=2$ and $y=3$ to get $\frac{4\cdot \cancel{3}}{\cancel{3}\cdot 2}=\frac{4}{2}=\boxed{2}.$
2
Level 3
Prealgebra
Problem: Simplify $\frac{8xy^2}{6x^2y}$ with $x=2$ and $y=3.$
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To simplify the expression, first substitute the values of $x$ and $y$ into the fraction. This gives us $\frac{8(2)(3^2)}{6(2^2)(3)}$. Next, calculate $3^2$, which equals $9$. Thus, the numerator becomes $8 \cdot 2 \cdot 9$. Calculate this step: $8 \cdot 2 = 16$, and then $16 \cdot 9 = 144$. 

Now, for the denominator, calculate $2^2$, which equals $4$. Therefore, the denominator becomes $6 \cdot 4 \cdot 3$. Calculate this step: $6 \cdot 4 = 24$, and then $24 \cdot 3 = 72$. 

Now we have the simplified fraction $\frac{144}{72}$. To simplify this further, divide both the numerator and the denominator by their greatest common divisor, which is $72$. 

Perform the division: $144 \div 72 = 2$ and $72 \div 72 = 1$. Thus, the simplified fraction is $\frac{2}{1}$, which equals $2$. 

Therefore, the final answer is $2$.<|END_OF_LATENT|> The final answer is $2$.