Writing Expressions in the form 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 $\,A^2\,$.
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 $\,A^2\,$.

Answer:

$9 = 3^2$

Question: Write

$\,9x^2\,$ in the form $\,A^2\,$.

Answer:

$9x^2 = 3^2x^2 = (3x)^2$

Question: Write

$\,x^6\,$ in the form $\,A^2\,$.

Answer:

$x^6 = x^{3\cdot 2} = (x^3)^2$

Question: Write

$\,16x^4\,$ in the form $\,A^2\,$.

Answer:

$16x^4 = 4^2\cdot x^{2\cdot 2} = 4^2 (x^2)^2 = (4x^2)^2$

Question: Write

$\,-16\,$ in the form $\,A^2\,$.

Answer: not possible; a negative number can't be a perfect square

Question: Write

$\,16x^3\,$ in the form $\,A^2\,$.

Answer: not possible using only whole numbers, since

$\,3\,$ 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

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.

If possible, write in the form $\,A^2\,$: