Chapter 4.4, Problem 28OE

To determine

To find: The square and cube of the expression $-4x^2{y}^2$ .

Answer to Problem 28OE

The square and cube of the expression $-4x^2{y}^2$ are $16x^4{y}^4$ and $-64x^6{y}^6$ respectively.

Explanation of Solution

Given:

The expression is $-4x^2{y}^2$ .

Calculation:

Square the given expression $-4x^2{y}^2$ as follows:

  $\begin{array}{c}{\left(-4x^2{y}^2\right)}^2=\left(-4x^2{y}^2\right)\times \left(-4x^2{y}^2\right)\\ =16\times x^{2+2}\times y^{2+2}\\ =16x^4{y}^4\end{array}$

Cube the given expression $-4x^2{y}^2$ as follows:

  $\begin{array}{c}{\left(-4x^2{y}^2\right)}^3=\left(-4x^2{y}^2\right)\times \left(-4x^2{y}^2\right)\times \left(-4x^2{y}^2\right)\\ =-64\times x^{2+2+2}\times y^{2+2+2}\\ =-64x^6{y}^6\end{array}$

Thus, the square and cube of the expression $-4x^2{y}^2$ are $16x^4{y}^4$ and $-64x^6{y}^6$ respectively.