To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, $a^m \times a^n=a^{m+n}$.
We have:
$\big(\frac{4}{3}\text{u}^2\text{vw}\big)×\big(−5\text{uvw}^2)×\big(\frac{1}{3}\text{v}^2\text{wu})$
$=\big[\frac{4}{3}×(−5)×\frac{1}{3}\big]×\big(\text{u}^2×\text{u}×\text{u}\big)$
$×\big(\text{v}×\text{v}×\text{v}^2)×\big(\text{w}×\text{w}^2×\text{w}\big)$
$=\big[\frac{4}{3}×(−5)×\frac{1}{3}\big]×\big(\text{u}^{2+1+1}\big)$
$×\big(\text{v}^{1+1+2}\big)×\big(\text{w}^{1+2+1}\big)$
$=−\frac{20}{9}\text{u}^4\text{v}^4\text{w}^4$
Thus, the answer is $=−\frac{20}{9}\text{u}^4\text{v}^4\text{w}^4$
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