What is $(15x^2) \cdot (6x) \cdot \left(\frac{1}{(3x)^2}\right)$?
Using the associative property and simplifying gives \begin{align*}
(15x^2) \cdot (6x) \cdot \left(\frac{1}{(3x)^2}\right)
&= (15 \cdot 6) \cdot (x^2 \cdot x) \cdot \left(\frac{1}{9x^2}\right)\\
&= \frac{90x^3}{9x^2}\\
&= 10x^{3-2} = \boxed{10x}.
\end{align*}
10x
Level 3
Algebra
Problem: What is $(15x^2) \cdot (6x) \cdot \left(\frac{1}{(3x)^2}\right)$?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To solve the expression, first simplify each component. Start with the term $(3x)^2$. This expands to $9x^2$. 

Next, rewrite the expression using this result: 
$(15x^2) \cdot (6x) \cdot \left(\frac{1}{9x^2}\right)$. 

Now, multiply the first two terms: 
$15x^2 \cdot 6x = 90x^3$. 

Now, substitute this back into the expression: 
$90x^3 \cdot \left(\frac{1}{9x^2}\right)$. 

This can be rewritten as: 
$\frac{90x^3}{9x^2}$. 

Next, simplify the fraction. Divide the coefficients: 
$\frac{90}{9} = 10$. 

Then, simplify the variable part: 
$\frac{x^3}{x^2} = x^{3-2} = x^1 = x$. 

Combining these results gives: 
$10x$. 

Thus, the final answer is $10x$.<|END_OF_LATENT|> The final answer is $10x$.