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
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$\,A^2\,$.
Only whole number coefficients and exponents are used in this exercise.
(The whole numbers are:
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$\,0, 1, 2, 3, \ldots\,$)
EXAMPLES:
Question:
Write
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$\,9\,$ in the form $\,A^2\,$.
Answer:
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$9 = 3^2$
Question:
Write
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$\,9x^2\,$ in the form $\,A^2\,$.
Answer:
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$9x^2 = 3^2x^2 = (3x)^2$
Question:
Write
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$\,x^6\,$ in the form $\,A^2\,$.
Answer:
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$x^6 = x^{3\cdot 2} = (x^3)^2$
Question:
Write
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$\,16x^4\,$ in the form $\,A^2\,$.
Answer:
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$16x^4 = 4^2\cdot x^{2\cdot 2} = 4^2 (x^2)^2 = (4x^2)^2$
Question:
Write
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$\,-16\,$ in the form $\,A^2\,$.
Answer:
not possible; a negative number can't be a perfect square
Question:
Write
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$\,16x^3\,$ in the form $\,A^2\,$.
Answer:
not possible using only whole numbers, since
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$\,3\,$ isn't a multiple of $\,2\,$