Chapter 4.3, Problem 3ST

To determine

To simplify: The given expression.

Answer to Problem 3ST

  $\left(3p^2\right){\left(-2p{q}^2\right)}^2$ is simplified as $12p^4{q}^4$ .

Explanation of Solution

Given:

The following expression:

  $\left(3p^2\right){\left(-2p{q}^2\right)}^2$

Formula used:

The second law of exponents:

  ${\left(ab\right)}^m=a^m{b}^m$

The first law of exponents:

  $a^m\cdot a=a^{m+n}$

Calculation:

The given expression can be simplified as:

  $\begin{array}{l}\left(3p^2\right){\left(-2p{q}^2\right)}^2[\text{Given]}\\ =\left(3p^2\right)\left[{\left(-2\right)}^2{\left(p\right)}^2{\left(q^2\right)}^2\right][\text{Second law of exponents]}\\ =\left(3p^2\right)\left(4p^2{q}^4\right)[\text{Simplify]}\\ =\left(3\cdot 4\right)\left(p^2\cdot p^2\right)q^4[\text{Combine similar terms]}\\ =12p^4{q}^4[\text{First law of exponents]}\end{array}$