Find product: (4 3 pq^2 )× (−1 4 p^2r )× (16p^2q^2r^2 )

Question

Find product:
$\big(\frac{4}{3}\text{pq}^2\big)×\big(\frac{−1}{4}\text{p}^2\text{r}\big)×\big(16\text{p}^2\text{q}^2\text{r}^2\big)$

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Answer

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:
$\big(\frac{4}{3}\text{pq}^2\big)×\big(\frac{−1}{4}\text{p}^2\text{r}\big)×\big(16\text{p}^2\text{q}^2\text{r}^2\big)$
$=\big[\frac{4}{3}×\big(\frac{−1}{4}\big)×16]×\big(\text{p}×\text{p}^2×\text{p}^2\big)\\×\big(\text{q}^2×\text{q}^2\big)×\big(\text{r}×\text{r}^2\big)$
$=\big[\frac{4}{3}×\big(\frac{−1}{4}\big)×16]×\big(\text{p}^{1+2+2}\big)×\big(\text{q}^{2+2}\big)×\big(\text{r}^{1+2}\big)$
$=−\frac{16}{3}\text{p}^5\text{q}^4\text{r}^3$
Thus, the answer is $=−\frac{16}{3}\text{p}^5\text{q}^4\text{r}^3$

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