Rewrite the value \(9^\frac{1}{2}\) as a root. Then, explain why \(9^\frac{1}{2} =3\).
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Problem 4
Another exponent rule states that \((mn)^p = m^p n^p\). For example, \((3x)^2 = 3^2 x^2 = 9x^2\), and \((xyz^2)^3 = x^3 y^3 (z^2)^3 = x^3 y^3 z^6\).
Use this rule to show why \(\sqrt[3]{x} \sqrt[3]{y} = \sqrt[3]{xy}\) by converting each side of the equation to its exponential form.
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Problem 5
\(3^5 = 243\)
Use this equation to write an expression equivalent to 3 using a root.
Use this equation to write an expression equivalent to 3 using an exponent.
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Problem 6
Complete the table so that each row has the same value in the different forms.
(Note that if you write something like \(\frac{1}{3}^2\), it is unclear if you mean \(\frac{1^2}{3} = \frac{1 \boldcdot 1}{3}\) or \(\left( \frac{1}{3} \right)^2 = \frac{1}{3} \boldcdot \frac{1}{3}\). Include parentheses if necessary.)
