WRITING EXPRESSIONS IN THE FORM [beautiful math coming... please be patient] $\,A^2\,$

For this lesson, you'll need to use 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 (say) $\,x^my^m\,$,
and rewriting it in the form $\,(xy)^m\,$.

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

EXAMPLES:
Question: Write [beautiful math coming... please be patient] $\,9\,$ in the form $\,A^2\,$.
Answer: [beautiful math coming... please be patient] $9 = 3^2$
Question: Write [beautiful math coming... please be patient] $\,9x^2\,$ in the form $\,A^2\,$.
Answer: [beautiful math coming... please be patient] $9x^2 = 3^2x^2 = (3x)^2$
Question: Write [beautiful math coming... please be patient] $\,x^6\,$ in the form $\,A^2\,$.
Answer: [beautiful math coming... please be patient] $x^6 = x^{3\cdot 2} = (x^3)^2$
Question: Write [beautiful math coming... please be patient] $\,16x^4\,$ in the form $\,A^2\,$.
Answer: [beautiful math coming... please be patient] $16x^4 = 4^2\cdot x^{2\cdot 2} = 4^2 (x^2)^2 = (4x^2)^2$
Question: Write [beautiful math coming... please be patient] $\,-16\,$ in the form $\,A^2\,$.
Answer: not possible; a negative number can't be a perfect square
Question: Write [beautiful math coming... please be patient] $\,16x^3\,$ in the form $\,A^2\,$.
Answer: not possible using only whole numbers, since [beautiful math coming... please be patient] $\,3\,$ isn't a multiple of $\,2\,$
Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Factoring a Difference of Squares

 
 
CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
Only whole number coefficients and exponents are used in this exercise.
PROBLEM TYPES:
1 2 3 4 5 6 7
AVAILABLE MASTERED IN PROGRESS
If possible, write in the form $\,A^2\,$: