Chapter 4.5, Problem 7MRE

To determine

To simplify the expression

  $2\cdot 3^3+2\cdot 3$

Answer to Problem 7MRE

  $60$

Explanation of Solution

Given:

  $2\cdot 3^3+2\cdot 3$

Concept Used:

• For all positive integers m : $\left(a^m\right)=a\times a\dots \times a\text{}m\text{-times}$

  If an expression contains more than one operations between its terms and brackets, first solve the terms inside brackets and then apply division followed by multiplication, addition and subtraction.

Calculation:

To simplify the expression

  $2\cdot 3^3+2\cdot 3$

Use the basic properties of power.

First simplify this using the property $\left(a^m\right)=a\times a\dots \times a\text{}m\text{-times}$ , and then proceed further to simplify, as

  $2\cdot 3^3+2\cdot 3=2\cdot 27+2\cdot 3$

Multiply the terms and then add:

  $\begin{array}{c}2\cdot 3^3+2\cdot 3=2\cdot 27+2\cdot 3\\ =\text{54+6}\\ =60\end{array}$

Thus, simplified form of given expression is

  $2\cdot 3^3+2\cdot 3=60$