Chapter 4, Problem 1RE

To determine

the simplified expression written with positive exponents.

Answer to Problem 1RE

Solution:

The simplified form is given by

$243x^5$

Explanation of Solution

Given:

  ${(3x)}^3{(3x)}^2$

Formula Used:

The Rule of Exponent $(x^a)(x^b)=x^{a+b}$ has been used here.

Calculation:

We have been given the expression ${(3x)}^3{(3x)}^2$. In order to write the simplified expression with positive exponent, we will perform below mentioned steps.

  $\begin{array}{l}{(}^3{(}^3\left(\text{Given expression}\right)\\ ={(}^3\left(\text{Use the rule (}{x}^a)(x^b)=x^{a+b}\right)\\ ={(}^3\left(\text{Simplify}\right)\\ =(3^5)(x^5)\\ =243x^5\end{array}$

Therefore the simplified form is given by

$243x^5$

Conclusion:

Using the rules of exponents, the simplified form is given by

$243x^5$