We need to calculate: the simplified form of (3sqrt[3]{a^{3}}(-5sqrt[4]{a^{3}}))

We need to calculate: the simplified form of $\left(3\sqrt[3]{{a}^{3}}\left(-5\sqrt[4]{{a}^{3}}\right)\right)$
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Given:
$\left(3\sqrt[3]{{a}^{3}}\left(-5\sqrt[4]{{a}^{3}}\right)\right)$
Used formula:
For a real number a when m is even,
$\sqrt[m]{{a}^{n}}=|{a}^{\frac{n}{m}}|$
Calculation:
$\left(3\sqrt[3]{{a}^{3}}\left(-5\sqrt[4]{{a}^{3}}\right)\right)$

Apply property of exponents:

Rewrite the expression with rational exponent: