Question

Find each of the following product: \[\left( \frac{4}{3}p q^2 \right) \times \left( - \frac{1}{4} p^2 r \right) \times \left( 16 p^2 q^2 r^2 \right)\]

Answer 1

To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., \[a^m \times a^n = a^{m + n}\].

We have:

\[\left( \frac{4}{3}p q^2 \right) \times \left( - \frac{1}{4} p^2 r \right) \times \left( 16 p^2 q^2 r^2 \right)\]

\[ = \left\{ \frac{4}{3} \times \left( - \frac{1}{4} \right) \times 16 \right\} \times \left( p \times p^2 \times p^2 \right) \times \left( q^2 \times q^2 \right) \times \left( r \times r^2 \right)\]

\[ = \left\{ \frac{4}{3} \times \left( - \frac{1}{4} \right) \times 16 \right\} \times \left( p^{1 + 2 + 2} \right) \times \left( q^{2 + 2} \right) \times \left( r^{1 + 2} \right)\]

\[ = - \frac{16}{3} p^5 q^4 r^3\]

Thus, the answer is \[- \frac{1}{3} p^5 q^4 r^3\].