Chapter 4.7, Problem 7MRE

To determine

To simplify the expression $n^2\cdot n^2\cdot n^2$ .

Answer to Problem 7MRE

  $n^6$

Explanation of Solution

Given information:

The expression, $n^2\cdot n^2\cdot n^2$

Concept used:

Exponent property: $a^n\cdot a^m=a^{n+m}$

Calculation:

In order to simplify the given expression $n^2\cdot n^2\cdot n^2$ , use the exponent property and simplify further as shown below

  $\begin{array}{c}{n}^2\cdot n^2\cdot n^2=\left(n^2\cdot n^2\right)\cdot n^2\\ =\left(n^{2+2}\right)\cdot n^2\\ =\left(n^4\right)\cdot n^2\\ =n^4\cdot n^2\\ =n^{4+2}\\ =n^6\end{array}$

Thus, the given expression simplifies to $n^6$ .