Chapter 4.3, Problem 27WE

To determine

To Simplify: The expression $\left(3p^{3}q\right)\left(-\frac{5}{6}{q}^3\right)\left(-p^4\right)$

Answer to Problem 27WE

The required answer is $\frac{5}{2}{p}^7{q}^4$ .

Explanation of Solution

Given information:

The expression $\left(3p^{3}q\right)\left(-\frac{5}{6}{q}^3\right)\left(-p^4\right)$

Concept Used:

Rule of exponents for product of powers states that to multiply two powers with same base, the exponents are added.

For example $a^m\cdot a^n=a^{m+n}$

Commutative property of multiplication states that the product of any numbers remains the same irrespective of the order in which we multiply.

For example:

  $2\cdot 5=5\cdot 2=10$

Associative property of multiplication states that the product of the any numbers remains the same regardless of the grouping of factors.

For example:

  $2\left(5\cdot 3\right)=\left(2\cdot 5\right)\cdot 3=30$

Calculation:

  $\left(3p^{3}q\right)\left(-\frac{5}{6}{q}^3\right)\left(-p^4\right)$

Commutative and Associative property of multiplication.

  $=\left(3\cdot \left(-\frac{5}{6}\right)\cdot \left(-1\right)\right)\left(p^3\cdot p^4\right)\left(q\cdot q^3\right)$

Using rule of exponents for product of powers

  $\begin{array}{l}=\frac{5}{2}\left(p^{3+4}\right)\left(q^{1+3}\right)\\ =\frac{5}{2}{p}^7{q}^4\end{array}$