Chapter SH, Problem 9.6.11EP

To determine

  ${\left(-x^{2}y{z}^3\right)}^6$ need to simplify.

Answer to Problem 9.6.11EP

  ${\left(-x^{2}y{z}^3\right)}^6=-y^6{x}^{12}{z}^{12}$

Explanation of Solution

Given:

  ${\left(-x^{2}y{z}^3\right)}^6$

Concept Used:

Product rule:

  ${\left(ab\right)}^m=a^m{b}^m$

Powers of power property:

  ${\left(a^m\right)}^n=a^{mn}$

Calculation:

The given number is: ${\left(-x^{2}y{z}^3\right)}^6$

By using the product rule:

  ${\left(ab\right)}^m=a^m{b}^m$

Put the given values:

  ${\left(-x^{2}y{z}^3\right)}^6=-y^6{\left(x^2\right)}^6{\left(z^2\right)}^6$

Use powers of power property:

  ${\left(a^m\right)}^n=a^{mn}$

Put the given values:

  $\begin{array}{l}{\left(-x^{2}y{z}^3\right)}^6=-y^6{\left(x^2\right)}^6{\left(z^2\right)}^6\\ {\left(-x^{2}y{z}^3\right)}^6=-y^6{x}^{2\times 6}{z}^{2\times 6}\\ {\left(-x^{2}y{z}^3\right)}^6=-y^6{x}^{12}{z}^{12}\end{array}$

Conclusion:

Hence, ${\left(-x^{2}y{z}^3\right)}^6=-y^6{x}^{12}{z}^{12}$ .