Simplify.

To simplify the expression \(\sqrt{3x^4}\cdot\sqrt{5x^2}\cdot\sqrt{10}\), we first use the property of square roots that states \(\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}\). Thus, we can combine the square roots under a single square root:

\[
\sqrt{3x^4} \cdot \sqrt{5x^2} \cdot \sqrt{10} = \sqrt{3x^4 \cdot 5x^2 \cdot 10}
\]

Now we calculate the product inside the square root:

\[
3 \cdot 5 \cdot 10 = 150
\]
\[
x^4 \cdot x^2 = x^{4+2} = x^6
\]

Combining these results gives us:

\[
\sqrt{3x^4 \cdot 5x^2 \cdot 10} = \sqrt{150x^6}
\]

Next, we can separate the expression inside the square root into perfect squares and the remaining factors:

\[
\sqrt{150x^6} = \sqrt{150} \cdot \sqrt{x^6}
\]

The term \(\sqrt{x^6}\) can be simplified further since \(x^6\) is a perfect square:

\[
\sqrt{x^6} = x^{6/2} = x^3
\]

Now, we will simplify \(\sqrt{150}\). We start by finding the prime factorization of 150:

\[
150 = 2 \cdot 3 \cdot 5^2
\]

The perfect square in this case is \(5^2\). Thus, we can simplify \(\sqrt{150}\):

\[
\sqrt{150} = \sqrt{2 \cdot 3 \cdot 5^2} = \sqrt{5^2} \cdot \sqrt{2 \cdot 3} = 5 \cdot \sqrt{6}
\]

Putting this all together, we have:

\[
\sqrt{150} \cdot x^3 = 5 \sqrt{6} \cdot x^3
\]

Thus, the final simplified form of our original expression is:

\[
\boxed{5x^3\sqrt{6}}
\]