Chapter 6.8, Problem 1PT

To determine

To calculate: The simplified form of ${\left(3a\right)}^2{\left(7b\right)}^4$ ,

Answer to Problem 1PT

The simplified form of ${\left(3a\right)}^2{\left(7b\right)}^4$ is $21609a^2{b}^4$ .

Explanation of Solution

Given information:

The statement “ ${\left(3a\right)}^2{\left(7b\right)}^4$ .”

Formula used:

When two or more functions are in multiplication then first open the power of the function and then multiply both functions, then solve the expression.

Consider the provided statement “ ${\left(3a\right)}^2{\left(7b\right)}^4$ .”

Recall that When two or more functions are in multiplication then first open the power of the function and then multiply both functions, then solve the expression

So, the given expression can be simplified as,

  ${\left(3a\right)}^2{\left(7b\right)}^4$

Observe to solve the expression first resolve the powers:

  ${\left(3a\right)}^2{\left(7b\right)}^4=\left(9a^2\right)\left(2401b^2\right)$ .

Now multiply the constants:

  $\begin{array}{c}{\left(3a\right)}^2{\left(7b\right)}^4=\left(9a^2\right)\left(2401b^2\right)\\ =21609a^2{b}^4\end{array}$

Since, $21609a^2{b}^4$ cannot be simplified further,

Hence, the simplified form of ${\left(3a\right)}^2{\left(7b\right)}^4$ is $21609a^2{b}^4$ .