1. The given expression is $49x^{3/2}$. 2. We want to simplify or understand this expression better. 3. Note that $49$ is a perfect square: $49 = 7^2$. 4. Rewrite the expression as $7^2 \cdot x^{3/2}$. 5. Recall the rules of exponents: $a^m \cdot a^n = a^{m+n}$ and $(a^m)^n = a^{mn}$. 6. The expression can be seen as $7^2 \times (x^{1/2})^3$, since $x^{3/2} = (x^{1/2})^3$. 7. $x^{1/2}$ is the square root of $x$, so we have $7^2 \cdot (\sqrt{x})^3$. 8. Therefore, the simplified form is $$49 \sqrt{x}^3 = 49 x^{3/2}$$. Final answer: $49 x^{3/2}$ (already simplified).