﻿ Writing Expressions in the form A^2

# Writing Expressions in the form $A^2$

Need some simpler practice with perfect squares first?

For this lesson, you'll need these exponent laws:

$(xy)^m = x^m y^m$
$(x^m)^n = x^{mn}$

You'll be using them ‘backwards’ that is, from right-to-left. That is, you'll be starting with an expression of the form $\,x^my^m\,,$ and rewriting it in the form $\,(xy)^m\,.$ Or, you'll be starting with an expression of the form $\,x^{mn}\,,$ and rewriting it in the form $\,(x^m)^n\,.$

Here, you will practice writing expressions in the form $\,A^2\,.$ Only whole number coefficients and exponents are used in this exercise. (The whole numbers are: $\,0,\, 1,\, 2,\, 3,\, \ldots\,$)

## Examples

Question: Write $\,9\,$ in the form $\,\color{red}{A}^2\,.$
Answer: $9 = \color{red}{3}^2$
Question: Write $\,9x^2\,$ in the form $\,\color{red}{A}^2\,.$
Answer: $9x^2 = 3^2x^2 = (\color{red}{3x})^2$
Question: Write $\,x^6\,$ in the form $\,\color{red}{A}^2\,.$
Answer: $x^6 = x^{3\cdot 2} = (\color{red}{x^3})^2$
Question: Write $\,16x^4\,$ in the form $\,\color{red}{A}^2\,.$
$\cssId{s31}{16x^4} \cssId{s32}{= 4^2\cdot x^{2\cdot 2}} \cssId{s33}{= 4^2 (x^2)^2} \cssId{s34}{= (\color{red}{4x^2})^2}$
Question: Write $\,-16\,$ in the form $\,A^2\,.$
Question: Write $\,16x^3\,$ in the form $\,A^2\,.$
Answer: not possible using only whole numbers, since $\,3\,$ isn't a multiple of $\,2\,$
If possible, write in the form $\,A^2\,$: