Chapter 7.3, Problem 65PPE

To determine

To find: Whether the given expression be written by using one exponent or not.

Answer to Problem 65PPE

Yes, the expression $49x^2{y}^2{z}^2$ can be written by using one exponent as ${\left(7xyz\right)}^2$ .

Explanation of Solution

Given information: The given expression is $49x^2{y}^2{z}^2$ .

Calculation:

The given expression is:

  $49x^2{y}^2{z}^2$

The factors of $49$ are:

  $\begin{array}{c}49=7\times 7\\ ={\left(7\right)}^2\end{array}$

Substitute ${\left(7\right)}^2$ for $49$ in the above given expression.

  $49x^2{y}^2{z}^2={\left(7\right)}^2{x}^2{y}^2{z}^2$

The multiplication property of exponent having different base and same power is:

  ${\left(ab\right)}^n=a^n{b}^n$

Use the above property in the above given expression.

  $49x^2{y}^2{z}^2={\left(7xyz\right)}^2$

Therefore, from the above expression it can be concluded that it is possible to write the given expression using only one exponent.